Review ArticleRecent Fuzzy Generalisations of RoughSets Theory A Systematic Review and MethodologicalCritique of the Literature

Abbas Mardani1 Mehrbakhsh Nilashi23 Jurgita Antucheviciene4

Madjid Tavana56 Romualdas Bausys7 and Othman Ibrahim2

1Faculty of Management Universiti Teknologi Malaysia (UTM) 81310 Skudai Johor Malaysia2Faculty of Computing Universiti Teknologi Malaysia 81310 Skudai Johor Malaysia3Department of Computer Engineering Lahijan Branch Islamic Azad University Lahijan Iran4Department of Construction Management and Real Estate Vilnius Gediminas Technical UniversitySauletekio Al 11 LT-10223 Vilnius Lithuania5Business Systems and Analytics Department La Salle University Philadelphia PA 19141 USA6Business Information Systems Department Faculty of Business Administration and EconomicsUniversity of Paderborn 33098 Paderborn Germany7Department of Graphical Systems Vilnius Gediminas Technical University Sauletekio Ave 11 LT-10223 Vilnius Lithuania

Correspondence should be addressed to Jurgita Antucheviciene jurgitaantuchevicienevgtult

Received 12 April 2017 Revised 23 August 2017 Accepted 10 September 2017 Published 29 October 2017

Academic Editor Danilo Comminiello

Copyright copy 2017 Abbas Mardani et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Rough set theory has been used extensively in fields of complexity cognitive sciences and artificial intelligence especially innumerous fields such as expert systems knowledge discovery information system inductive reasoning intelligent systems datamining pattern recognition decision-making and machine learning Rough sets models which have been recently proposed aredeveloped applying the different fuzzy generalisations Currently there is not a systematic literature review and classification ofthese new generalisations about rough set models Therefore in this review study the attempt is made to provide a comprehensivesystematic review of methodologies and applications of recent generalisations discussed in the area of fuzzy-rough set theory Onthis subject the Web of Science database has been chosen to select the relevant papers Accordingly the systematic and meta-analysis approach which is called ldquoPRISMArdquo has been proposed and the selected articles were classified based on the author andyear of publication author nationalities application field type of study study category study contribution and journal in which thearticles have appeared Based on the results of this review we found that there are many challenging issues related to the differentapplication area of fuzzy-rough set theory which can motivate future research studies

1 Introduction

Rough set theory is a powerful and popularmachine learningmethod [1] It is particularly appropriate for dealing withinformation systems that exhibit inconsistencies [2] Fuzzy-rough set theory can be integrated with the rough set theoryto handle data with continuous attributes and can detectinconsistencies in the data Because the fuzzy-rough setmodel is a powerful tool in analysing inconsistent and vaguedata it has proven to be very useful inmany application areas

Rough set theory introduced by Pawlak [3] in the 1980s is apowerful machine learning tool that has applications inmanydata mining [4ndash11] instances attribute and feature selection[12ndash25] and data prediction [26 27] Rough set theory dealswith information systems that contain inconsistent data suchas two patients who have the same symptoms but differentdiseases In the rough set analysis data is expected to be dis-crete Therefore a continuous numeric attribute is requiredto be discretized Fuzzy-rough set theory [28] is an extensionof the rough set theory that deals with continuous numerical

HindawiComplexityVolume 2017 Article ID 1608147 33 pageshttpsdoiorg10115520171608147

2 Complexity

attributes It can solve the same problems that rough set cansolve and also can handle both numerical and discrete dataThe importance of fuzzy-rough set theory is clearly seen inseveral applications areas For example Wang [29] andWang[30] investigated topological characterizations of generalisedfuzzy-rough sets in the context of basic rough equalities Panet al [31] enhanced the fuzzy preference relation rough setmodel with an additive consistent fuzzy preference relationNamburu et al [32] suggested the soft fuzzy-rough set-basedmagnetic resonance brain image segmentation for handlingthe uncertainty related to indiscernibility and vagueness Liet al [33] proposed an effective fuzzy-rough set model forfeature selection Feng et al [34] used uncertainty measuresfor reduction of multigranulation based on fuzzy-rough setsavoiding the negative and positive regions Sun et al [35] pre-sented three kinds of multigranulation fuzzy-rough sets overtwo universes using a constructivemethod Zhao andHu [36]examined a decision-theoretic rough set model in the contextof models of interval-valued fuzzy and fuzzy probabilisticapproximation spaces Zhang and Shu [37] suggested a newparadigm based on generalised interval-valued fuzzy-roughsets by combining the theory of rough sets and theory ofinterval-valued fuzzy sets based on axiomatic and construc-tive methods Zhang et al [24] proposed a new fuzzy-roughset theory based on information entropy for feature selectionWang and Hu [38] proposed arbitrary fuzzy relations byintegrating granular variable precision fuzzy-rough sets andgeneral fuzzy relations Vluymans et al [19] suggested a newkind of classifier for imbalanced multi-instance data basedon fuzzy-rough set theory Feng and Mi [39] investigatedand reviewed the variable precision ofmultigranulation fuzzydecision-theoretic rough sets in an information systemWangand Hu [40] presented novel generalised L-fuzzy-rough setsfor generalisation of the notion of L-fuzzy-rough sets

In recent decades various kinds of models have beenproposed and developed regarding the fuzzy generalisationof rough set theory However the literature review has notkept pace with the rapid addition of knowledge in this fieldTherefore we believe that there is a need for a systematicconsideration of the most relevant recent studies conductedin this area This review paper attempts to systematicallyreview the previous studies that proposed or developed fuzzy-rough sets theory This review paper adds significant insightinto the literature of fuzzy-rough set theory by consideringsome new perspectives in examining the articles such asthe classification of the papers based on author and yearof publication author nationalities application field type ofstudy study category study contribution and the journals inwhich they appear

The structure of this review study is organised as followsSection 2 shortly reviews the literature regarding fuzzylogic and fuzzy sets rough sets fuzzy set theory fuzzylogical operators fuzzy relations rough set theory andfuzzy-rough set theory In Section 3 we present the relatedworks Section 4 presents research methodology includingthe systematic review meta-analysis and the procedures ofthis study Section 5 provides findings of this review basedon the application areas Section 6 presents the distributionof papers by the journals In Section 7 we present the

distribution of papers by the year of publication Section 8presents the distribution of papers based on the nationality ofauthors Section 9 discusses the results of this review with thefocus on the recent fuzzy generalisation of rough sets theoryand further investigations in this area Finally Section 10presents the conclusion limitations and recommendationsfor future studies

2 Fuzzy-Rough Sets Theory

21 Fuzzy Logic and Fuzzy Sets Binary logic is discrete andhas only two logic values which are true and false that is 1and 0 In real-life however things are true to some extent Forexample regarding the patient there are some assumptionssuch as patient is sick or say patient is very sick or startingto become sick Therefore we cannot confidently say if thepatient is sick or not with a certain intensity Fuzzy logic [43]has extended binary logic through adding an intensity rangeof values to specify the extent to which something is true Inthis situation the range of truth values is between 0 and 1The closer the truth value of a statement to 1 the truer thestatement For example the patient is very sick could havethe degree of sickness around 09 to specify that the patient isvery sick On the other side patient could have the sicknessdegree of 01 indicating that the patient is nearly recoveredfrom the illness A fuzzy set [44] is a set of factors that fit to theset with the membership degree For instant we assume thatthere are two fuzzy sets representing two groups of peopleincluding old and young peopleThus the larger the age of oneperson the higher the membership degree to the old peopleand the lower the person membership degree to the youngpeople Meanwhile fuzzy logic is extending the binary logicand moreover extends its logical operations These are the t-conorm fuzzy logical 119905-norm and implicator [45] that extendthe binary logical implication conjunction and disjunction

22 Rough Sets In the very big datasets with several itemscalculating the gradual indiscernibility relation is very chal-lenging in terms of memory and runtime Rough set theory(Pawlak [46] Polkowski et al [47]) is the novel mathematicstechnique dealing with uncertain and inexact knowledgein several applications in various real-life fields such asinformation analysis medicine and data mining Rough setis the powerful machine learning technique which has beenused in many application areas such as feature selectionprediction instance selection and decision-making Roughset also has applications in many areas such as medical dataanalysis image processing finance and many other real-lifeproblems [3] A rough set approximates a certain set of factorswith two subsets including upper approximations and lowerapproximations The fuzzy-rough set theory is constructedbased on two theories including rough set theory and fuzzyset theory In the next section we present these theories withhybridisation of both theories

23 Fuzzy SetTheory Zadeh [44] found that traditional crispset is not capable of explaining the whole thing in the realmanner Zadeh proposed fuzzy sets to solve this problemTherefore Zadeh proposed a fuzzy set 119860 as a mapping from

Complexity 3

the universe 119880 to the interval [0 1] The set 119860(119909) for 119909 isin 119880is called the degree of membership of 119909 in 119860 Employ thismethod factors in the universe could belong to a set to acertain degree Discovery for the good fuzzy set for modelconcepts could be subjective and challenging however itis more significant than trying to create an artificial crispdistinction among factors Indeed that fuzzy set was anextension of crisp set Consequently any crisp set 119860 could bemodelled using a fuzzy set as follows

forall119909 isin 119880 119860 (119909) =

10

forall119909 isin 119880 119860 (119909) =

1 if119909 isin 1198600 else

(1)

The cardinality of a fuzzy set 119860 is defined as the sum ofthe membership values of all factors in the universe to 119860

|119860| = sum119909isin119880

119860 (119909) (2)

24 Fuzzy Logical Operators There is need for the new logicaloperators to extend the crisp sets to the fuzzy sets In crisp settheory for example the proposition a factor belongs to thesets119860 and119861 is either true or false For extending this theoremto fuzzy set theory there is need to the fuzzy logical operatorsfor extending the logical conjunction and for expressing towhat extent an example 119909 belongs to 119860 and 119861 given themembership degrees 119860(119909) and 119861(119909)

The conjunction and and the disjunction or were extendedby using the t-conorm S and t-norm T that map T 119878 [0 1]2 rarr [0 1] satisfying the following conditions

T and S are increasing in both argumentsT and S are commutativeT and S are associative

forall119909 isin 119880 T (119909 1) = 119909forall119909 isin 119880 120575 (119909 0) = 119909

(3)

The most significant examples of t-norms are the mini-mum operator 120591119872 which is the largest t-norm the productoperatorT119875 and the Łukasiewicz t-normT119871

forall119909 119910 isin (0 1) T119872 (119909 119910) = min (119909 119910)

forall119909 119910 isin (0 1) T119875 (119909 119910) = 119909119910

forall119909 119910 isin (0 1) T119871 (119909 119910) = max (0 119909 + 119910 minus 1)

(4)

The important examples of t-conorms are the maximumoperatorS119872 which is the smallest t-conorm the probabilis-tic sum S119901 and the Łukasiewicz t-conorm S119871

forall119909 119910 isin (0 1) S119872 (119909 119910) = max (119909 119910)

forall119909 119910 isin (0 1) S119901 (119909 119910) = 119909 + 119910 minus 119909119910

forall119909 119910 isin (0 1) S119871 (119909 119910) = min (1 119909 + 119910)

(5)

The implication rarr is extended by fuzzy implicatorswhich are mappings T [0 1]2 rarr [0 1] that satisfy thefollowing

119871 is decreasing in the first and increasing in the secondargument119871 satisfies 119871(1 1) = 119871(0 0) = 1 and 119871(1 0) = 0

The well-knowing implicator is the Łukasiewicz implica-tor 119871119871 defined by

forall119909 119910 isin (0 1) 119871119871 (119909 119910) = min (1 1 minus 119909 + 119910) (6)

25 Fuzzy Relations The binary fuzzy relations in 119880 are thespecial type of fuzzy sets which are fuzzy sets 119877 in 1198802 andexpress to what extent 119909 and 119910 are associated with othersIn the field of fuzzy-rough set usually use relations formodelling indiscernibility between the examples Thereforewe refer to them as indiscernibility relations We need 119877 tobe minimum a fuzzy tolerance relation that is 119877 is reflexiveforall119909 isin 119880 119877(119909 119909) = 1 and symmetric forall119909 119910 isin 119880 119877(119909 119910) =119877(119910 119909)

These two situations are linked to the symmetry andreflexivity conditions of the equivalence relation The thirdsituation for an equivalence relation transitivity is translatedtoT-transitivity for a certain t-normT

forall119909 119910 119911 isin T (119877 (119909 119910) 119877 (119910 119911)) le 119877 (119909 119911) (7)

For this case 119877 is called a T-similarity relation Thuswhen 119877 is T119872-transitive 119877 is T-transitive for all t-normsT For this case 119877 will be a similarity relation

26 Rough Set Theory Pawlak [3] proposed the rough settheory for handling the problem of incomplete informa-tion Pawlak introduced a universe 119880 involving factorsan equivalence relation 119877 on 119880 and a concept 119860 sube 119880within the universe The problem of incomplete informationindicates that it should not be possible to determine theconcept 119860 based on the equivalence relation 119877 which isthere are two factors 119909 and 119910 in 119880 that are equivalent to119877 but to which 119909 belongs to 119860 and 119910 does not Figure 1represented this case in which the universe is divided intosquares applying the equivalence relation The concept 119860does not follow the lines of the squares which means that119860 cannot be described using 119877 In real world this kind ofproblem with incomplete information often occurs such asproblem of spam classification For example we assume theworld contains nonspam and spam e-mails and mention thatthis concept is spam The equivalence relation is introducedaccording to the predefined list of 10 words which usuallyare in the spam e-mails thus it can mention that two e-mails are equivalent if they have the similar words among thelist of 10 words Some equivalence classes will be completelycontained in the spam group and some will be completelycontained in the nonspam group Though it is very likelythat there are two e-mails that have the similar words amongthe list of 10 words however for which one is spam and theother is nonspam In this case the equivalence relation is not

4 Complexity

A

U

Equivalence class with respect to R

Figure 1 A universe119880 partitioned by an equivalence relation 119877 anda concept 119860 sube 119880 that cannot be defined using 119877 [41 42]

able to distinguish between spam and nonspam Pawlak [3]addressed this kind of problem by approximating the concept119860 The lower approximation includes all the equivalenceclasses that are included in 119860 and the upper approximationincludes the equivalence classes for which at least one factoris in 119860 Figure 2 represented the concept of lower and upperapproximations

An equivalence relation is reflexive thus 119909 is onlyincluded in 119877 darr 119860 if 119909 isin 119860 The upper approximation isdefined by

119877 uarr 119860 = 119909 isin 119880 | exist119910 isin 119880 (119909 119910) isin 119877 and 119910 isin 119860 (8)

The lower approximation of 119860 using 119877 is defined asfollows

119877 darr 119910 = 119909 isin 119880 | forall119910 isin 119880 (119909 119910) isin 119877 997888rarr 119910 isin 119860 (9)

The lower approximation in the spam example containsall e-mails that are spam and for which all e-mails indis-cernible from it are also spam The upper approximationcontains of e-mails that are spam and e-mails that arenonspam but for which there exists an e-mail indiscerniblefrom it that is spam

27 Fuzzy-Rough Set Theory Fuzzy set theory enables us tomodel vague information while rough set theory modelsincomplete information These two theories are not com-peting but rather complement each other Many modelshave been proposed to hybridise rough sets and fuzzy sets[6 29 30 34 39 170ndash178] A fuzzy-rough set is the pair oflower and upper approximations of a fuzzy set119860 in a universe119880 on which a fuzzy relation 119877 is defined The fuzzy-roughmodel is obtained by fuzzifying the definitions of the crisplower and upper approximation Recall that the condition foran element 119909 isin 119880 to belong to the crisp lower approximationis

forall119910 isin 119880 (119909 119910) isin 119877 997888rarr 119910 isin 119860 (10)

The equivalence relation 119877 is now a fuzzy relation and119860 is a fuzzy set The values 119877(119909 119910) and 119860(119910) are connectedby a fuzzy implication L so L(119877(119909 119910) 119860(119910)) expresses towhat extent elements that are similar to 119909 belong to 119860

The membership value of an element 119909 isin 119880 to the lowerapproximation is high if these values L(119877(119909 119910) 119860(119910)) arehigh for all 119910 isin 119860

forall119909 isin 119880 (119877 darr 119860) (119909) = min119910isin119880

L (119877 (119909 119910) 119860 (119910))

forall119909 isin 119880 (119877 uarr 119860) (119909) = max119910isin119880

T (119877 (119909 119910) 119860 (119910)) (11)

This upper approximation expresses to what extent thereexist instances that are similar to 119909 and belong to 119860

3 Related Works

Morsi and Yakout [179] examined the relationship betweenfuzzy-rough sets theory based on 119877-implicators and left-continuous 119905-norms with focus on fuzzy similarity in theaxiomatic approachWang andHong [180] proposed an algo-rithm to produce a set of fuzzy rules from noisy quantitativetraining data by applying the variable precision rough setmodel Molodtsov [181] employed the theory of rough setsin several ways and formulated the soft number notions softintegral and soft derivative Maji et al [182] examined thesoft sets in detail and provided the application of soft setsin decision-making by employing the rough sets reductionRadzikowska and Kerre [28] investigated the family of fuzzy-rough sets based on fuzzy implicators which were calledgeneralised fuzzy-rough sets De Cock et al [183] introducedfuzzy-rough sets based on 119877-foresets of all objects withrespect to a fuzzy binary relation when 119877 is a fuzzy serialrelation Jensen and Shen [184] proposed classical roughsets based on a dependency function of fuzzy-rough setsand presented the new greedy algorithm for reduction ofredundant attributes Mieszkowicz-Rolka and Rolka [185]proposed an approach based on the variable precision fuzzy-rough set approach to the analysis of noisy data Mi andZhang [186] introduced a new fuzzy-rough set definitionbased on a residual implication 120579 and its dual 120590 Shen andJensen [187] proposed an approach that integrates a fuzzy ruleinduction algorithm with a fuzzy-rough method for featureselection Wu et al [188] examined generalised fuzzy-roughsets in the axiomaticmethod Bhatt andGopal [189] proposeda new concept of compact computational domain for Jensenrsquosalgorithm for enhancing computational efficiency Yeung etal [190] proposed some fuzzy-rough set models by meansof arbitrary fuzzy relations and investigated the connectionsbetween the existing fuzzy-rough sets Deng et al [191] inves-tigated fuzzy relations by involving a fuzzy covering Li andMa [192] proposed two pairs of fuzzy-rough approximationoperators including fuzzy and crisp covering-based fuzzy-rough approximation operators Aktas and Cagman [193]compared the concepts of rough sets soft sets and fuzzysets and showed that for each fuzzy set rough set is a softset Greco et al [194] integrated the DTRS approach withthe dominance-based rough set approach and presented anew generalised rough set theory approach Cornelis et al[195] introduced a classical rough set approach by utilisingfuzzy tolerance relations considering fuzzy-rough set theoryWang et al [196] introduced new definitions of fuzzy lower

Complexity 5

A

U

(a) The lower approximation

s

A

U

(b) The upper approximation

Figure 2 The concept 119860 is approximated by means of the lower and upper approximations [41 42]

and upper approximations by using the similarity betweentwo objects Hu et al [197] proposed a novel fuzzy-roughset model based on which a straightforward and efficienthybrid attribute reduction algorithm was designed Lingraset al [198] and Lingras et al [199] applied the DTRS theoryfor clustering analysis She and Wang [200] investigated L-fuzzy-rough set theory from an axiomatic method Zhao etal [201] suggested the new concept based on fuzzy variableprecision rough sets for handling the noise of perturbationand misclassification Wu et al [202] introduced a newattribute reduction approach focusing on the interval type2 fuzzy-rough set model and providing some properties ofinterval type 2 fuzzy-rough sets Yan et al [203] proposedgeneralising the rough set model with fuzzy relation on twouniverses using fuzzy theory and probabilistic methods Yangand Yao [204] investigated the multiagent DTRS model Xuet al [205] examined the GRS approach based on the roughmembership function Xia and Xu [206] investigated intu-itionistic fuzzy information changing Wu [207] examinedfuzzy-rough sets based on 119905-norms and discussed algebraicstructures and fuzzy topologies Feng et al [208] suggestedthe soft rough sets concept instead of equivalence classesand defined the parameterized soft set of upper and lowerapproximations Meng et al [209] suggested an approach forcalculating the upper and lower approximations for fuzzy softsets which efficiently define the boundary Li and Zhou [210]and Li et al [211] suggested a multiperspective explanationof the decision-theoretic rough set approach and attributereduction Jia et al [212] investigated the problem related toattribute reduction for decision-theoretic rough set theoryLiu et al [213] and Liu et al [214] explored multiple-categoryclassification with the DTRS method and applications inmanagement science Degang et al [215] introduced a novelapproach to examine fuzzy-rough sets by integrating gran-ular computing Hu et al [94] used kernel functions forintroducing the fuzzy similarity relations and developed thegreedy algorithm based on dimensionality reduction Maand Sun [216] proposed a probabilistic rough set model ontwo universes Ma and Sun [217] investigated the decision-theoretic rough set theory over two universes based on theidea of classical DTRS theory Liu et al [218] studied the GRSapproach based on twouniverses and discussed its propertiesChen et al [102] used fuzzy-rough sets to present a matrix

of fuzzy discernibility Zhang et al [111] proposed a generalframework of intuitionistic fuzzy-rough sets and discussedthe intuitionistic fuzzy operator and the properties of themodel with the dual domain caseWei et al [219] investigatedthe relationships among rough approximations of fuzzy-rough setmodels Chen et al [117] explored the interpretationof several types of membership functions geometricallyby using the lower approximations in fuzzy-rough sets interms of square distances in Krein spaces Ma and Hu [220]examined lattice structures and the topology of L-fuzzy-rough sets by considering upper and lower approximationssets Yang et al [70] suggested a fuzzy probabilistic roughset model on two universes Liang et al [59] examinedinformation retrieval and filtering by employing the DTRStheory Zhang and Miao [221] and Zhang and Miao [222]proposed the double-quantitative approximation space forpresenting two double-quantitative rough set theories Yaoet al [101] suggested the variable precision (120579 120590)-fuzzy-rough sets theory regarding fuzzy granules Liu et al [223]investigated logistic regression for classification based ondecision-theoretic rough sets theory Ma et al [224] sug-gested a decision region distribution preservation reductionin decision-theoretic rough set theory Qian et al [225]investigated the multigranulation decision-theoretic roughset approach Sun et al [82] examined the DTRFS applicationandmodel Zhang andMiao [226] constructed a fundamentalreduction framework for two-category decision-theoreticrough sets Gong and Zhang [105] investigated a method ofintuitionistic fuzzy sets and variable precision rough sets toconstruct an extended intuitionistic fuzzy-rough set modelZhao and Xiao [131] defined the general type-2 fuzzy-roughsets and discussed the basic properties of lower and upperapproximation operators Zhang and Miao [227] and Zhangand Miao [228] examined attribute reduction for proposingrough set theory models Drsquoeer et al [118] investigatedthe drawbacks and benefits of implicatorndashconjunctor-basednoise-tolerant fuzzy-rough set models Li and Cui [77]studied the characterizations of the topology of fuzzy-roughsets by considering the similarity of fuzzy relations Li andCui [229] investigated fuzzy topologies considering a lowerfuzzy-rough approximation operator based on the t-conormXu et al [230] introduced a knowledge reduction approach ina generalised approximation space over two universes Li and

6 Complexity

Xu [231] introduced the multigranulation decision-theoreticrough set approach in the ordered information systemLiang et al [232] suggested three-way decisions by extendingthe DTRS approach to a qualitative environment Ju et al[233] presented a moderate attribute reduction model inDTRS Li and Xu [234] investigated the double-quantitativeDTRS approach based on assembling the upper and lowerapproximations of the GRS and DTRS methods Wang [114]examined type 2 fuzzy-rough sets by considering two finiteuniverses and utilising axiomatic and constructive methodsand investigated some topological properties of type 2 fuzzy-rough sets Zhang and Min [235] used three-way decisionsregarding recommender systems Wang [114] defined anupper approximation number for developing a quantitativeanalysis of covering-based rough set theory Wang et al [25]proposed a fitting fuzzy-rough set model to conduct featureselection Yang and Hu [178] proposed a definition of fuzzy120573-covering approximation spaces by introducing some newdefinitions of fuzzy 120573-covering approximation spaces Marsquosfuzzy covering-based rough set and the properties of fuzzy120573-covering approximation spaces Wang [29] investigatedcharacterizations of generalised fuzzy-rough sets in the corerough equalities context Namburu et al [32] suggested a softfuzzy-rough set-based segmentation of magnetic resonancebrain image for handling the uncertainty regarding the indis-cernibility and vagueness in a parameterized representationWang [30] examined the topological structures of L-fuzzy-rough set theory Liang et al [232] examined triangular fuzzydecision-theoretic rough sets Zhang andYao [236] examinedfunctions of the Gini objective for three-way classificationSun et al [237] explored three-way group decision-making byusing multigranulation fuzzy decision-theoretic rough setsFeng et al [34] investigated reduction of themultigranulationfuzzy information system based on uncertainty measuresby considering variable precision multigranulation decision-theoretic fuzzy-rough set theory and avoiding the changingof negative region and positive region to small ones Sun etal [62] proposed the new fuzzy-rough set on a probabilisticapproximation space and used it with respect to decision-making in unconventional emergency management Hu etal [171] proposed a new incremental method to updateapproximations of fuzzy information system over two uni-verses Fan et al [72] introduced several double-quantitativeDTRS (DQ-DTRFS) models based on logical conjunctionand disjunction operations Qiao and Hu [238] proposed agranular variable precision L-fuzzy-rough set theory basedon residuated lattices with arbitrary L-fuzzy relations Lianget al [172] examined the decision principles of three-waydecision rules based on the variation of loss functions withIFSs

4 Research Method

For the research methodology in this study we used thePreferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) provided byMoher et al [239] PRISMAhas two main parts including systematic reviews and meta-analyses Systematic reviews provide objective summaries ofwhat has been written and found out about research topics

This is especially valuable in wide research areas wheremany publications exist each focusing on a narrow aspectof the field [240] Systematic reviews aim to provide a fulloverview of research conducted in a specific area until thepresent date All research procedures have to bemade explicitbefore the actual behaviour of the review to make the processobjective and replicable Meta-analysis provides a meansof mathematically integrating findings employing diversestatistical approaches to study the diversity of the articlesIn this kind of synthesis original studies that are compatiblewith their quality level are selected This aspect may help andhighlight different facts which individual primary studies failto do for example it may prove that results are statisticallysignificant and relevant when small primary studies provideinconclusive and uncertain results with a large confidenceinterval [241] The main goal of PRISMA is to help theresearchers and practitioners complete a comprehensive andclear literature review [242]

Several previous studies have been conducted usingPRISMA in the various fields to develop a comprehensiveliterature review [242ndash244] In order to implement thePRISMA method in this study we accomplish three mainsteps including literature search choosing the eligible pub-lished papers and extraction of data and summarising [237]

41 Literature Search In this step we have chosen the Webof Science database to provide a comprehensive applicationof fuzzy-rough set theories The literature search was accom-plished based on two keywords including rough set theoriesand fuzzy-rough set theories We attempted to collect thecurrent published papers from 2010 to 2016 In the first stepof our search we found 5648 scholarly papers related tothe rough set theories and fuzzy-rough set theories whichwere extracted according to our strategy search In the nextstep we searched to find the papers which were publishedbetween 2010 and 2016 and checked the duplicate paperswith redundant information After this step 296 papers wereremaining After removing 17 records due to duplicationwe screened papers based on the titles and abstracts andirrelevant papers were removed In total 193 potentiallyrelated papers remained (see Figure 3)

42 Articles Eligibility In this step of the review for thepurpose of eligibility we reviewed the full text of each articleindependently (which extracted from the last step) In thelast step we carefully identified the related articles to attaina consensus Book chapters unpublished working paperseditorial notes master dissertations and doctoral thesestextbooks and non-English papers were excluded In the endwe selected 132 articles related to the fuzzy-rough sets from28 international scholarly journals between 2010 and 2016whichmet our inclusion criteriaWe selected the papers from2010 because of such a large number of papers published inthis field

43 Data Extraction and Summarising In the final step ofour methodology after negotiation with other authors somerequired information was collected and finally 132 articleswere reviewed and summarised In Table 1 all the selected

Complexity 7

Scre

enin

gIn

clude

dEl

igib

ility

Search in Web of Science for rough sets theories (n = 4856)

Search in Web of Science for fuzzy-rough sets theories (n = 792)

Search in databases for fuzzy-rough sets from 2010 to 2016 (n = 296)

Removed records due to duplicates (n = 17)

Screened records based of abstract review (n = 279)

Excluded records based of abstract review (n = 86)

Assessed full-text articles for eligibility (n = 193)

Excluded full-text articles with reasons (n = 71)

Studies included in qualitative synthesis (n = 122)

Identified papers in references (n = 10)

Included articles for meta-analysis (n = 132)

Iden

tifica

tion

Figure 3 Study flowchart for the identification screening eligibility and inclusion of articles

Table 1 Classification of papers based on application area

Application areas Frequency Percentage of frequencyInformation systems 12 909Decision-making 9 833Approximation operators 15 1136Feature and attribute selection 24 2045Fuzzy set theories 37 2727Other application areas 35 2348Total 132 10000

articles were classified into different classifications includinginformation systems decision-making approximate reason-ing feature and attribute selection machine learning fuzzyset theories and other application areas Also the articleswere summarised and reviewed based on the various criteriasuch as author and year of publication author nationalitiesapplication field type of study study category study contri-bution and journal in which they appeared We believe thatreviewing summarising and classifying the articles helped us

to achieve some critical and valuable insights Consequentlysome suggestions and recommendations for future studieswere proposed Furthermore we believe that this reviewpaper was accomplished very carefully and it presented acomprehensive source regarding the fuzzy-rough set theoriesIt should be noted that the main difficulty of using thePRISMA method was to understand what methodologieswere used from the abstract and the research section of theselected articles Thus we required going through the full

8 Complexity

content of articles and took a more detailed look to evaluatethe exactly applied approach to evaluate the fuzzy-roughsets Although a considerable amount of time was spent inthe selection process it helped us choose the most suitablepublications in conducting the review

5 Application Areas Classification

Although categorising and combining the articles in the fieldsof fuzzy-rough sets is complex for the classification taskwe used the opinions of experts Consequently based onopinions of experts we categorised articles into six differentapplications areas (see Table 1) In the following section allselected articles were summarised and reviewed based on thevarious criteria

51 Distribution Papers Based on Information Systems Roughset theory is a powerful and popular machine learningmethod It is particularly appropriate for dealing with theinformation systems that exhibit inconsistencies Fuzzy settheory integrated with the rough set theory detects degreesof inconsistency in the data Xu et al [245] examined a newparallel attribute reduction algorithm by focusing on fuzzy-rough set theory and mutual information rather than calcu-lating of the fuzzy-rough lower and upper approximationsexplicitlyMoreover Yang et al [246] investigated some roughsets models for handling big data but this study does notfocus on explicitly calculating the upper and lower approx-imations Some previous scholars investigated the parallelmodels for computing the upper and lower approximationsin the traditional rough set model For example Zhang etal [247] introduced a new MapReduce-based approach forcalculating the upper and lower approximations in a decisionsystem Zhang et al [248] used different approximationsto compare knowledge acquisition Yang and Chen [249]suggested a novel approach to calculate the positive regionsuch as the union of the lower approximation of all classesDubois and Prade [250] explored the relationship similar-ities and differences between twofold fuzzy sets and roughsets Ouyang et al [50] defined new fuzzy rough sets whichgeneralized the concept of fuzzy rough sets in the senseof Radzikowska and Kerre [28] and that of Mi and Zhang[186] Kuznetsov et al [251] introduced an approach basedon the fuzzy-rough sets which were called the (119868 119869)-fuzzy-rough set Zeng et al [52] developed a new Hybrid Distance(HD) in Hybrid Information System (HIS) based on thevalue difference metric and a new fuzzy-rough approachwas designed by integrating the Gaussian kernel and HDdistance Feng and Mi [39] investigated variable precisionmultigranulation fuzzy decision-theoretic rough sets in aninformation system Chen et al [55] introduced a newapproach to build a polygonal rough-fuzzy set and presenteda novel fuzzy interpolative reasoning approach for sparsefuzzy rule-based systems based on the ratio of fuzziness of theconstructed polygonal rough-fuzzy sets Table 2 representssignificant distribution findings of information systems basedon the author and year of publication application field typeof study study category and study contribution The results

represented in this table indicate that 12 articles have beenpublished in the area of information systems

52 Distribution Papers Based on Decision-Making Whilethere are a variety of existing methods for various applicationareas from imprecise data the fuzzy-rough set method hasan advantage for decision-making for large volumes of datasince it focuses on reducing the number of attributes requiredto characterize a concept without losing essential informationrequired for decision-making Although rough sets have sev-eral advantages over other methods they generate a numberof rules creating difficulties in decision-making [252] Afuzzy-rough set is a data mining algorithm for decision-making based on incomplete inconsistent imprecise andvague data Fuzzy-rough set theory is an extension of thefuzzy conventional set theory that supports approximationsin decision-making However rough set theories are valu-able mathematical approaches for explaining and showinginsufficient and incomplete information and also have beenextensively used in numerous application areas such ascomprehensive evaluation and uncertainty decision-makingwith fuzzy information [62] Greco et al [253] proposed anew dominance rough set framework that is appropriate forpreference analysis [31 254ndash261] This study investigated thedecision-making problem with multicriteria and attributeswhere dominance relations are extracted from similarity rela-tions andmulticriteria are created from equivalence relationsand numerical attributes are created from nominal attributesAn extensive review of multicriteria decision analysis basedon dominance rough sets is given in Greco et al [253]Dominance rough sets have also been applied to ordinalattribute reduction [253 262] and multicriteria classification[263ndash266] Recently several previous studies extended thefuzzy set based on the dominance rough set approach[106 170 258 267 268] Hu et al [60] proposed a novelapproach for extracting the fuzzy preference relations byusing a fuzzy-rough set model Liang and Liu [61] presenteda naive approach of intuitionistic fuzzy decision-theoreticrough sets (IFDTRSs) and analysed its related properties Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets The detailed results of this section are presented inTable 3 The findings represented in this table indicate that 8articles have been published in the area of decision-making

53 Distribution Papers Based on Approximation OperatorsA rough set approximates a crisp set by two other sets thatgive a lower and upper approximation of the crisp set Inthe rough set analysis the data is expected to be discrete Inenormous information systems the computation of the lowerand upper approximation sets is a demanding process bothregarding processing time and memory utilisation A roughset approximates a certain set of elements with two othersubsets called upper and lower approximations Through thefuzzy-rough lower and upper approximation fuzzy-rough settheory can model the quality or typicality of instances withintheir respective classes and hence it is an ideal tool to detectborder points and noisy instances The lower approximation

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical PhysicsAdvances in

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Discrete Dynamics in Nature and Society

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Complexity 3

the universe 119880 to the interval [0 1] The set 119860(119909) for 119909 isin 119880is called the degree of membership of 119909 in 119860 Employ thismethod factors in the universe could belong to a set to acertain degree Discovery for the good fuzzy set for modelconcepts could be subjective and challenging however itis more significant than trying to create an artificial crispdistinction among factors Indeed that fuzzy set was anextension of crisp set Consequently any crisp set 119860 could bemodelled using a fuzzy set as follows

forall119909 isin 119880 119860 (119909) =

10

forall119909 isin 119880 119860 (119909) =

1 if119909 isin 1198600 else

(1)

The cardinality of a fuzzy set 119860 is defined as the sum ofthe membership values of all factors in the universe to 119860

|119860| = sum119909isin119880

119860 (119909) (2)

24 Fuzzy Logical Operators There is need for the new logicaloperators to extend the crisp sets to the fuzzy sets In crisp settheory for example the proposition a factor belongs to thesets119860 and119861 is either true or false For extending this theoremto fuzzy set theory there is need to the fuzzy logical operatorsfor extending the logical conjunction and for expressing towhat extent an example 119909 belongs to 119860 and 119861 given themembership degrees 119860(119909) and 119861(119909)

The conjunction and and the disjunction or were extendedby using the t-conorm S and t-norm T that map T 119878 [0 1]2 rarr [0 1] satisfying the following conditions

T and S are increasing in both argumentsT and S are commutativeT and S are associative

forall119909 isin 119880 T (119909 1) = 119909forall119909 isin 119880 120575 (119909 0) = 119909

(3)

The most significant examples of t-norms are the mini-mum operator 120591119872 which is the largest t-norm the productoperatorT119875 and the Łukasiewicz t-normT119871

forall119909 119910 isin (0 1) T119872 (119909 119910) = min (119909 119910)

forall119909 119910 isin (0 1) T119875 (119909 119910) = 119909119910

forall119909 119910 isin (0 1) T119871 (119909 119910) = max (0 119909 + 119910 minus 1)

(4)

The important examples of t-conorms are the maximumoperatorS119872 which is the smallest t-conorm the probabilis-tic sum S119901 and the Łukasiewicz t-conorm S119871

forall119909 119910 isin (0 1) S119872 (119909 119910) = max (119909 119910)

forall119909 119910 isin (0 1) S119901 (119909 119910) = 119909 + 119910 minus 119909119910

forall119909 119910 isin (0 1) S119871 (119909 119910) = min (1 119909 + 119910)

(5)

The implication rarr is extended by fuzzy implicatorswhich are mappings T [0 1]2 rarr [0 1] that satisfy thefollowing

119871 is decreasing in the first and increasing in the secondargument119871 satisfies 119871(1 1) = 119871(0 0) = 1 and 119871(1 0) = 0

The well-knowing implicator is the Łukasiewicz implica-tor 119871119871 defined by

forall119909 119910 isin (0 1) 119871119871 (119909 119910) = min (1 1 minus 119909 + 119910) (6)

25 Fuzzy Relations The binary fuzzy relations in 119880 are thespecial type of fuzzy sets which are fuzzy sets 119877 in 1198802 andexpress to what extent 119909 and 119910 are associated with othersIn the field of fuzzy-rough set usually use relations formodelling indiscernibility between the examples Thereforewe refer to them as indiscernibility relations We need 119877 tobe minimum a fuzzy tolerance relation that is 119877 is reflexiveforall119909 isin 119880 119877(119909 119909) = 1 and symmetric forall119909 119910 isin 119880 119877(119909 119910) =119877(119910 119909)

These two situations are linked to the symmetry andreflexivity conditions of the equivalence relation The thirdsituation for an equivalence relation transitivity is translatedtoT-transitivity for a certain t-normT

forall119909 119910 119911 isin T (119877 (119909 119910) 119877 (119910 119911)) le 119877 (119909 119911) (7)

For this case 119877 is called a T-similarity relation Thuswhen 119877 is T119872-transitive 119877 is T-transitive for all t-normsT For this case 119877 will be a similarity relation

26 Rough Set Theory Pawlak [3] proposed the rough settheory for handling the problem of incomplete informa-tion Pawlak introduced a universe 119880 involving factorsan equivalence relation 119877 on 119880 and a concept 119860 sube 119880within the universe The problem of incomplete informationindicates that it should not be possible to determine theconcept 119860 based on the equivalence relation 119877 which isthere are two factors 119909 and 119910 in 119880 that are equivalent to119877 but to which 119909 belongs to 119860 and 119910 does not Figure 1represented this case in which the universe is divided intosquares applying the equivalence relation The concept 119860does not follow the lines of the squares which means that119860 cannot be described using 119877 In real world this kind ofproblem with incomplete information often occurs such asproblem of spam classification For example we assume theworld contains nonspam and spam e-mails and mention thatthis concept is spam The equivalence relation is introducedaccording to the predefined list of 10 words which usuallyare in the spam e-mails thus it can mention that two e-mails are equivalent if they have the similar words among thelist of 10 words Some equivalence classes will be completelycontained in the spam group and some will be completelycontained in the nonspam group Though it is very likelythat there are two e-mails that have the similar words amongthe list of 10 words however for which one is spam and theother is nonspam In this case the equivalence relation is not

4 Complexity

A

U

Equivalence class with respect to R

Figure 1 A universe119880 partitioned by an equivalence relation 119877 anda concept 119860 sube 119880 that cannot be defined using 119877 [41 42]

able to distinguish between spam and nonspam Pawlak [3]addressed this kind of problem by approximating the concept119860 The lower approximation includes all the equivalenceclasses that are included in 119860 and the upper approximationincludes the equivalence classes for which at least one factoris in 119860 Figure 2 represented the concept of lower and upperapproximations

An equivalence relation is reflexive thus 119909 is onlyincluded in 119877 darr 119860 if 119909 isin 119860 The upper approximation isdefined by

119877 uarr 119860 = 119909 isin 119880 | exist119910 isin 119880 (119909 119910) isin 119877 and 119910 isin 119860 (8)

The lower approximation of 119860 using 119877 is defined asfollows

119877 darr 119910 = 119909 isin 119880 | forall119910 isin 119880 (119909 119910) isin 119877 997888rarr 119910 isin 119860 (9)

The lower approximation in the spam example containsall e-mails that are spam and for which all e-mails indis-cernible from it are also spam The upper approximationcontains of e-mails that are spam and e-mails that arenonspam but for which there exists an e-mail indiscerniblefrom it that is spam

27 Fuzzy-Rough Set Theory Fuzzy set theory enables us tomodel vague information while rough set theory modelsincomplete information These two theories are not com-peting but rather complement each other Many modelshave been proposed to hybridise rough sets and fuzzy sets[6 29 30 34 39 170ndash178] A fuzzy-rough set is the pair oflower and upper approximations of a fuzzy set119860 in a universe119880 on which a fuzzy relation 119877 is defined The fuzzy-roughmodel is obtained by fuzzifying the definitions of the crisplower and upper approximation Recall that the condition foran element 119909 isin 119880 to belong to the crisp lower approximationis

forall119910 isin 119880 (119909 119910) isin 119877 997888rarr 119910 isin 119860 (10)

The equivalence relation 119877 is now a fuzzy relation and119860 is a fuzzy set The values 119877(119909 119910) and 119860(119910) are connectedby a fuzzy implication L so L(119877(119909 119910) 119860(119910)) expresses towhat extent elements that are similar to 119909 belong to 119860

The membership value of an element 119909 isin 119880 to the lowerapproximation is high if these values L(119877(119909 119910) 119860(119910)) arehigh for all 119910 isin 119860

forall119909 isin 119880 (119877 darr 119860) (119909) = min119910isin119880

L (119877 (119909 119910) 119860 (119910))

forall119909 isin 119880 (119877 uarr 119860) (119909) = max119910isin119880

T (119877 (119909 119910) 119860 (119910)) (11)

This upper approximation expresses to what extent thereexist instances that are similar to 119909 and belong to 119860

3 Related Works

Morsi and Yakout [179] examined the relationship betweenfuzzy-rough sets theory based on 119877-implicators and left-continuous 119905-norms with focus on fuzzy similarity in theaxiomatic approachWang andHong [180] proposed an algo-rithm to produce a set of fuzzy rules from noisy quantitativetraining data by applying the variable precision rough setmodel Molodtsov [181] employed the theory of rough setsin several ways and formulated the soft number notions softintegral and soft derivative Maji et al [182] examined thesoft sets in detail and provided the application of soft setsin decision-making by employing the rough sets reductionRadzikowska and Kerre [28] investigated the family of fuzzy-rough sets based on fuzzy implicators which were calledgeneralised fuzzy-rough sets De Cock et al [183] introducedfuzzy-rough sets based on 119877-foresets of all objects withrespect to a fuzzy binary relation when 119877 is a fuzzy serialrelation Jensen and Shen [184] proposed classical roughsets based on a dependency function of fuzzy-rough setsand presented the new greedy algorithm for reduction ofredundant attributes Mieszkowicz-Rolka and Rolka [185]proposed an approach based on the variable precision fuzzy-rough set approach to the analysis of noisy data Mi andZhang [186] introduced a new fuzzy-rough set definitionbased on a residual implication 120579 and its dual 120590 Shen andJensen [187] proposed an approach that integrates a fuzzy ruleinduction algorithm with a fuzzy-rough method for featureselection Wu et al [188] examined generalised fuzzy-roughsets in the axiomaticmethod Bhatt andGopal [189] proposeda new concept of compact computational domain for Jensenrsquosalgorithm for enhancing computational efficiency Yeung etal [190] proposed some fuzzy-rough set models by meansof arbitrary fuzzy relations and investigated the connectionsbetween the existing fuzzy-rough sets Deng et al [191] inves-tigated fuzzy relations by involving a fuzzy covering Li andMa [192] proposed two pairs of fuzzy-rough approximationoperators including fuzzy and crisp covering-based fuzzy-rough approximation operators Aktas and Cagman [193]compared the concepts of rough sets soft sets and fuzzysets and showed that for each fuzzy set rough set is a softset Greco et al [194] integrated the DTRS approach withthe dominance-based rough set approach and presented anew generalised rough set theory approach Cornelis et al[195] introduced a classical rough set approach by utilisingfuzzy tolerance relations considering fuzzy-rough set theoryWang et al [196] introduced new definitions of fuzzy lower

Complexity 5

A

U

(a) The lower approximation

s

A

U

(b) The upper approximation

Figure 2 The concept 119860 is approximated by means of the lower and upper approximations [41 42]

and upper approximations by using the similarity betweentwo objects Hu et al [197] proposed a novel fuzzy-roughset model based on which a straightforward and efficienthybrid attribute reduction algorithm was designed Lingraset al [198] and Lingras et al [199] applied the DTRS theoryfor clustering analysis She and Wang [200] investigated L-fuzzy-rough set theory from an axiomatic method Zhao etal [201] suggested the new concept based on fuzzy variableprecision rough sets for handling the noise of perturbationand misclassification Wu et al [202] introduced a newattribute reduction approach focusing on the interval type2 fuzzy-rough set model and providing some properties ofinterval type 2 fuzzy-rough sets Yan et al [203] proposedgeneralising the rough set model with fuzzy relation on twouniverses using fuzzy theory and probabilistic methods Yangand Yao [204] investigated the multiagent DTRS model Xuet al [205] examined the GRS approach based on the roughmembership function Xia and Xu [206] investigated intu-itionistic fuzzy information changing Wu [207] examinedfuzzy-rough sets based on 119905-norms and discussed algebraicstructures and fuzzy topologies Feng et al [208] suggestedthe soft rough sets concept instead of equivalence classesand defined the parameterized soft set of upper and lowerapproximations Meng et al [209] suggested an approach forcalculating the upper and lower approximations for fuzzy softsets which efficiently define the boundary Li and Zhou [210]and Li et al [211] suggested a multiperspective explanationof the decision-theoretic rough set approach and attributereduction Jia et al [212] investigated the problem related toattribute reduction for decision-theoretic rough set theoryLiu et al [213] and Liu et al [214] explored multiple-categoryclassification with the DTRS method and applications inmanagement science Degang et al [215] introduced a novelapproach to examine fuzzy-rough sets by integrating gran-ular computing Hu et al [94] used kernel functions forintroducing the fuzzy similarity relations and developed thegreedy algorithm based on dimensionality reduction Maand Sun [216] proposed a probabilistic rough set model ontwo universes Ma and Sun [217] investigated the decision-theoretic rough set theory over two universes based on theidea of classical DTRS theory Liu et al [218] studied the GRSapproach based on twouniverses and discussed its propertiesChen et al [102] used fuzzy-rough sets to present a matrix

of fuzzy discernibility Zhang et al [111] proposed a generalframework of intuitionistic fuzzy-rough sets and discussedthe intuitionistic fuzzy operator and the properties of themodel with the dual domain caseWei et al [219] investigatedthe relationships among rough approximations of fuzzy-rough setmodels Chen et al [117] explored the interpretationof several types of membership functions geometricallyby using the lower approximations in fuzzy-rough sets interms of square distances in Krein spaces Ma and Hu [220]examined lattice structures and the topology of L-fuzzy-rough sets by considering upper and lower approximationssets Yang et al [70] suggested a fuzzy probabilistic roughset model on two universes Liang et al [59] examinedinformation retrieval and filtering by employing the DTRStheory Zhang and Miao [221] and Zhang and Miao [222]proposed the double-quantitative approximation space forpresenting two double-quantitative rough set theories Yaoet al [101] suggested the variable precision (120579 120590)-fuzzy-rough sets theory regarding fuzzy granules Liu et al [223]investigated logistic regression for classification based ondecision-theoretic rough sets theory Ma et al [224] sug-gested a decision region distribution preservation reductionin decision-theoretic rough set theory Qian et al [225]investigated the multigranulation decision-theoretic roughset approach Sun et al [82] examined the DTRFS applicationandmodel Zhang andMiao [226] constructed a fundamentalreduction framework for two-category decision-theoreticrough sets Gong and Zhang [105] investigated a method ofintuitionistic fuzzy sets and variable precision rough sets toconstruct an extended intuitionistic fuzzy-rough set modelZhao and Xiao [131] defined the general type-2 fuzzy-roughsets and discussed the basic properties of lower and upperapproximation operators Zhang and Miao [227] and Zhangand Miao [228] examined attribute reduction for proposingrough set theory models Drsquoeer et al [118] investigatedthe drawbacks and benefits of implicatorndashconjunctor-basednoise-tolerant fuzzy-rough set models Li and Cui [77]studied the characterizations of the topology of fuzzy-roughsets by considering the similarity of fuzzy relations Li andCui [229] investigated fuzzy topologies considering a lowerfuzzy-rough approximation operator based on the t-conormXu et al [230] introduced a knowledge reduction approach ina generalised approximation space over two universes Li and

6 Complexity

Xu [231] introduced the multigranulation decision-theoreticrough set approach in the ordered information systemLiang et al [232] suggested three-way decisions by extendingthe DTRS approach to a qualitative environment Ju et al[233] presented a moderate attribute reduction model inDTRS Li and Xu [234] investigated the double-quantitativeDTRS approach based on assembling the upper and lowerapproximations of the GRS and DTRS methods Wang [114]examined type 2 fuzzy-rough sets by considering two finiteuniverses and utilising axiomatic and constructive methodsand investigated some topological properties of type 2 fuzzy-rough sets Zhang and Min [235] used three-way decisionsregarding recommender systems Wang [114] defined anupper approximation number for developing a quantitativeanalysis of covering-based rough set theory Wang et al [25]proposed a fitting fuzzy-rough set model to conduct featureselection Yang and Hu [178] proposed a definition of fuzzy120573-covering approximation spaces by introducing some newdefinitions of fuzzy 120573-covering approximation spaces Marsquosfuzzy covering-based rough set and the properties of fuzzy120573-covering approximation spaces Wang [29] investigatedcharacterizations of generalised fuzzy-rough sets in the corerough equalities context Namburu et al [32] suggested a softfuzzy-rough set-based segmentation of magnetic resonancebrain image for handling the uncertainty regarding the indis-cernibility and vagueness in a parameterized representationWang [30] examined the topological structures of L-fuzzy-rough set theory Liang et al [232] examined triangular fuzzydecision-theoretic rough sets Zhang andYao [236] examinedfunctions of the Gini objective for three-way classificationSun et al [237] explored three-way group decision-making byusing multigranulation fuzzy decision-theoretic rough setsFeng et al [34] investigated reduction of themultigranulationfuzzy information system based on uncertainty measuresby considering variable precision multigranulation decision-theoretic fuzzy-rough set theory and avoiding the changingof negative region and positive region to small ones Sun etal [62] proposed the new fuzzy-rough set on a probabilisticapproximation space and used it with respect to decision-making in unconventional emergency management Hu etal [171] proposed a new incremental method to updateapproximations of fuzzy information system over two uni-verses Fan et al [72] introduced several double-quantitativeDTRS (DQ-DTRFS) models based on logical conjunctionand disjunction operations Qiao and Hu [238] proposed agranular variable precision L-fuzzy-rough set theory basedon residuated lattices with arbitrary L-fuzzy relations Lianget al [172] examined the decision principles of three-waydecision rules based on the variation of loss functions withIFSs

4 Research Method

For the research methodology in this study we used thePreferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) provided byMoher et al [239] PRISMAhas two main parts including systematic reviews and meta-analyses Systematic reviews provide objective summaries ofwhat has been written and found out about research topics

This is especially valuable in wide research areas wheremany publications exist each focusing on a narrow aspectof the field [240] Systematic reviews aim to provide a fulloverview of research conducted in a specific area until thepresent date All research procedures have to bemade explicitbefore the actual behaviour of the review to make the processobjective and replicable Meta-analysis provides a meansof mathematically integrating findings employing diversestatistical approaches to study the diversity of the articlesIn this kind of synthesis original studies that are compatiblewith their quality level are selected This aspect may help andhighlight different facts which individual primary studies failto do for example it may prove that results are statisticallysignificant and relevant when small primary studies provideinconclusive and uncertain results with a large confidenceinterval [241] The main goal of PRISMA is to help theresearchers and practitioners complete a comprehensive andclear literature review [242]

Several previous studies have been conducted usingPRISMA in the various fields to develop a comprehensiveliterature review [242ndash244] In order to implement thePRISMA method in this study we accomplish three mainsteps including literature search choosing the eligible pub-lished papers and extraction of data and summarising [237]

41 Literature Search In this step we have chosen the Webof Science database to provide a comprehensive applicationof fuzzy-rough set theories The literature search was accom-plished based on two keywords including rough set theoriesand fuzzy-rough set theories We attempted to collect thecurrent published papers from 2010 to 2016 In the first stepof our search we found 5648 scholarly papers related tothe rough set theories and fuzzy-rough set theories whichwere extracted according to our strategy search In the nextstep we searched to find the papers which were publishedbetween 2010 and 2016 and checked the duplicate paperswith redundant information After this step 296 papers wereremaining After removing 17 records due to duplicationwe screened papers based on the titles and abstracts andirrelevant papers were removed In total 193 potentiallyrelated papers remained (see Figure 3)

42 Articles Eligibility In this step of the review for thepurpose of eligibility we reviewed the full text of each articleindependently (which extracted from the last step) In thelast step we carefully identified the related articles to attaina consensus Book chapters unpublished working paperseditorial notes master dissertations and doctoral thesestextbooks and non-English papers were excluded In the endwe selected 132 articles related to the fuzzy-rough sets from28 international scholarly journals between 2010 and 2016whichmet our inclusion criteriaWe selected the papers from2010 because of such a large number of papers published inthis field

43 Data Extraction and Summarising In the final step ofour methodology after negotiation with other authors somerequired information was collected and finally 132 articleswere reviewed and summarised In Table 1 all the selected

Complexity 7

Scre

enin

gIn

clude

dEl

igib

ility

Search in Web of Science for rough sets theories (n = 4856)

Search in Web of Science for fuzzy-rough sets theories (n = 792)

Search in databases for fuzzy-rough sets from 2010 to 2016 (n = 296)

Removed records due to duplicates (n = 17)

Screened records based of abstract review (n = 279)

Excluded records based of abstract review (n = 86)

Assessed full-text articles for eligibility (n = 193)

Excluded full-text articles with reasons (n = 71)

Studies included in qualitative synthesis (n = 122)

Identified papers in references (n = 10)

Included articles for meta-analysis (n = 132)

Iden

tifica

tion

Figure 3 Study flowchart for the identification screening eligibility and inclusion of articles

Table 1 Classification of papers based on application area

Application areas Frequency Percentage of frequencyInformation systems 12 909Decision-making 9 833Approximation operators 15 1136Feature and attribute selection 24 2045Fuzzy set theories 37 2727Other application areas 35 2348Total 132 10000

articles were classified into different classifications includinginformation systems decision-making approximate reason-ing feature and attribute selection machine learning fuzzyset theories and other application areas Also the articleswere summarised and reviewed based on the various criteriasuch as author and year of publication author nationalitiesapplication field type of study study category study contri-bution and journal in which they appeared We believe thatreviewing summarising and classifying the articles helped us

to achieve some critical and valuable insights Consequentlysome suggestions and recommendations for future studieswere proposed Furthermore we believe that this reviewpaper was accomplished very carefully and it presented acomprehensive source regarding the fuzzy-rough set theoriesIt should be noted that the main difficulty of using thePRISMA method was to understand what methodologieswere used from the abstract and the research section of theselected articles Thus we required going through the full

8 Complexity

content of articles and took a more detailed look to evaluatethe exactly applied approach to evaluate the fuzzy-roughsets Although a considerable amount of time was spent inthe selection process it helped us choose the most suitablepublications in conducting the review

5 Application Areas Classification

Although categorising and combining the articles in the fieldsof fuzzy-rough sets is complex for the classification taskwe used the opinions of experts Consequently based onopinions of experts we categorised articles into six differentapplications areas (see Table 1) In the following section allselected articles were summarised and reviewed based on thevarious criteria

51 Distribution Papers Based on Information Systems Roughset theory is a powerful and popular machine learningmethod It is particularly appropriate for dealing with theinformation systems that exhibit inconsistencies Fuzzy settheory integrated with the rough set theory detects degreesof inconsistency in the data Xu et al [245] examined a newparallel attribute reduction algorithm by focusing on fuzzy-rough set theory and mutual information rather than calcu-lating of the fuzzy-rough lower and upper approximationsexplicitlyMoreover Yang et al [246] investigated some roughsets models for handling big data but this study does notfocus on explicitly calculating the upper and lower approx-imations Some previous scholars investigated the parallelmodels for computing the upper and lower approximationsin the traditional rough set model For example Zhang etal [247] introduced a new MapReduce-based approach forcalculating the upper and lower approximations in a decisionsystem Zhang et al [248] used different approximationsto compare knowledge acquisition Yang and Chen [249]suggested a novel approach to calculate the positive regionsuch as the union of the lower approximation of all classesDubois and Prade [250] explored the relationship similar-ities and differences between twofold fuzzy sets and roughsets Ouyang et al [50] defined new fuzzy rough sets whichgeneralized the concept of fuzzy rough sets in the senseof Radzikowska and Kerre [28] and that of Mi and Zhang[186] Kuznetsov et al [251] introduced an approach basedon the fuzzy-rough sets which were called the (119868 119869)-fuzzy-rough set Zeng et al [52] developed a new Hybrid Distance(HD) in Hybrid Information System (HIS) based on thevalue difference metric and a new fuzzy-rough approachwas designed by integrating the Gaussian kernel and HDdistance Feng and Mi [39] investigated variable precisionmultigranulation fuzzy decision-theoretic rough sets in aninformation system Chen et al [55] introduced a newapproach to build a polygonal rough-fuzzy set and presenteda novel fuzzy interpolative reasoning approach for sparsefuzzy rule-based systems based on the ratio of fuzziness of theconstructed polygonal rough-fuzzy sets Table 2 representssignificant distribution findings of information systems basedon the author and year of publication application field typeof study study category and study contribution The results

represented in this table indicate that 12 articles have beenpublished in the area of information systems

52 Distribution Papers Based on Decision-Making Whilethere are a variety of existing methods for various applicationareas from imprecise data the fuzzy-rough set method hasan advantage for decision-making for large volumes of datasince it focuses on reducing the number of attributes requiredto characterize a concept without losing essential informationrequired for decision-making Although rough sets have sev-eral advantages over other methods they generate a numberof rules creating difficulties in decision-making [252] Afuzzy-rough set is a data mining algorithm for decision-making based on incomplete inconsistent imprecise andvague data Fuzzy-rough set theory is an extension of thefuzzy conventional set theory that supports approximationsin decision-making However rough set theories are valu-able mathematical approaches for explaining and showinginsufficient and incomplete information and also have beenextensively used in numerous application areas such ascomprehensive evaluation and uncertainty decision-makingwith fuzzy information [62] Greco et al [253] proposed anew dominance rough set framework that is appropriate forpreference analysis [31 254ndash261] This study investigated thedecision-making problem with multicriteria and attributeswhere dominance relations are extracted from similarity rela-tions andmulticriteria are created from equivalence relationsand numerical attributes are created from nominal attributesAn extensive review of multicriteria decision analysis basedon dominance rough sets is given in Greco et al [253]Dominance rough sets have also been applied to ordinalattribute reduction [253 262] and multicriteria classification[263ndash266] Recently several previous studies extended thefuzzy set based on the dominance rough set approach[106 170 258 267 268] Hu et al [60] proposed a novelapproach for extracting the fuzzy preference relations byusing a fuzzy-rough set model Liang and Liu [61] presenteda naive approach of intuitionistic fuzzy decision-theoreticrough sets (IFDTRSs) and analysed its related properties Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets The detailed results of this section are presented inTable 3 The findings represented in this table indicate that 8articles have been published in the area of decision-making

53 Distribution Papers Based on Approximation OperatorsA rough set approximates a crisp set by two other sets thatgive a lower and upper approximation of the crisp set Inthe rough set analysis the data is expected to be discrete Inenormous information systems the computation of the lowerand upper approximation sets is a demanding process bothregarding processing time and memory utilisation A roughset approximates a certain set of elements with two othersubsets called upper and lower approximations Through thefuzzy-rough lower and upper approximation fuzzy-rough settheory can model the quality or typicality of instances withintheir respective classes and hence it is an ideal tool to detectborder points and noisy instances The lower approximation

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Complexity

A

U

Equivalence class with respect to R

Figure 1 A universe119880 partitioned by an equivalence relation 119877 anda concept 119860 sube 119880 that cannot be defined using 119877 [41 42]

able to distinguish between spam and nonspam Pawlak [3]addressed this kind of problem by approximating the concept119860 The lower approximation includes all the equivalenceclasses that are included in 119860 and the upper approximationincludes the equivalence classes for which at least one factoris in 119860 Figure 2 represented the concept of lower and upperapproximations

An equivalence relation is reflexive thus 119909 is onlyincluded in 119877 darr 119860 if 119909 isin 119860 The upper approximation isdefined by

119877 uarr 119860 = 119909 isin 119880 | exist119910 isin 119880 (119909 119910) isin 119877 and 119910 isin 119860 (8)

The lower approximation of 119860 using 119877 is defined asfollows

119877 darr 119910 = 119909 isin 119880 | forall119910 isin 119880 (119909 119910) isin 119877 997888rarr 119910 isin 119860 (9)

The lower approximation in the spam example containsall e-mails that are spam and for which all e-mails indis-cernible from it are also spam The upper approximationcontains of e-mails that are spam and e-mails that arenonspam but for which there exists an e-mail indiscerniblefrom it that is spam

27 Fuzzy-Rough Set Theory Fuzzy set theory enables us tomodel vague information while rough set theory modelsincomplete information These two theories are not com-peting but rather complement each other Many modelshave been proposed to hybridise rough sets and fuzzy sets[6 29 30 34 39 170ndash178] A fuzzy-rough set is the pair oflower and upper approximations of a fuzzy set119860 in a universe119880 on which a fuzzy relation 119877 is defined The fuzzy-roughmodel is obtained by fuzzifying the definitions of the crisplower and upper approximation Recall that the condition foran element 119909 isin 119880 to belong to the crisp lower approximationis

forall119910 isin 119880 (119909 119910) isin 119877 997888rarr 119910 isin 119860 (10)

The equivalence relation 119877 is now a fuzzy relation and119860 is a fuzzy set The values 119877(119909 119910) and 119860(119910) are connectedby a fuzzy implication L so L(119877(119909 119910) 119860(119910)) expresses towhat extent elements that are similar to 119909 belong to 119860

The membership value of an element 119909 isin 119880 to the lowerapproximation is high if these values L(119877(119909 119910) 119860(119910)) arehigh for all 119910 isin 119860

forall119909 isin 119880 (119877 darr 119860) (119909) = min119910isin119880

L (119877 (119909 119910) 119860 (119910))

forall119909 isin 119880 (119877 uarr 119860) (119909) = max119910isin119880

T (119877 (119909 119910) 119860 (119910)) (11)

This upper approximation expresses to what extent thereexist instances that are similar to 119909 and belong to 119860

3 Related Works

Morsi and Yakout [179] examined the relationship betweenfuzzy-rough sets theory based on 119877-implicators and left-continuous 119905-norms with focus on fuzzy similarity in theaxiomatic approachWang andHong [180] proposed an algo-rithm to produce a set of fuzzy rules from noisy quantitativetraining data by applying the variable precision rough setmodel Molodtsov [181] employed the theory of rough setsin several ways and formulated the soft number notions softintegral and soft derivative Maji et al [182] examined thesoft sets in detail and provided the application of soft setsin decision-making by employing the rough sets reductionRadzikowska and Kerre [28] investigated the family of fuzzy-rough sets based on fuzzy implicators which were calledgeneralised fuzzy-rough sets De Cock et al [183] introducedfuzzy-rough sets based on 119877-foresets of all objects withrespect to a fuzzy binary relation when 119877 is a fuzzy serialrelation Jensen and Shen [184] proposed classical roughsets based on a dependency function of fuzzy-rough setsand presented the new greedy algorithm for reduction ofredundant attributes Mieszkowicz-Rolka and Rolka [185]proposed an approach based on the variable precision fuzzy-rough set approach to the analysis of noisy data Mi andZhang [186] introduced a new fuzzy-rough set definitionbased on a residual implication 120579 and its dual 120590 Shen andJensen [187] proposed an approach that integrates a fuzzy ruleinduction algorithm with a fuzzy-rough method for featureselection Wu et al [188] examined generalised fuzzy-roughsets in the axiomaticmethod Bhatt andGopal [189] proposeda new concept of compact computational domain for Jensenrsquosalgorithm for enhancing computational efficiency Yeung etal [190] proposed some fuzzy-rough set models by meansof arbitrary fuzzy relations and investigated the connectionsbetween the existing fuzzy-rough sets Deng et al [191] inves-tigated fuzzy relations by involving a fuzzy covering Li andMa [192] proposed two pairs of fuzzy-rough approximationoperators including fuzzy and crisp covering-based fuzzy-rough approximation operators Aktas and Cagman [193]compared the concepts of rough sets soft sets and fuzzysets and showed that for each fuzzy set rough set is a softset Greco et al [194] integrated the DTRS approach withthe dominance-based rough set approach and presented anew generalised rough set theory approach Cornelis et al[195] introduced a classical rough set approach by utilisingfuzzy tolerance relations considering fuzzy-rough set theoryWang et al [196] introduced new definitions of fuzzy lower

Complexity 5

A

U

(a) The lower approximation

s

A

U

(b) The upper approximation

Figure 2 The concept 119860 is approximated by means of the lower and upper approximations [41 42]

and upper approximations by using the similarity betweentwo objects Hu et al [197] proposed a novel fuzzy-roughset model based on which a straightforward and efficienthybrid attribute reduction algorithm was designed Lingraset al [198] and Lingras et al [199] applied the DTRS theoryfor clustering analysis She and Wang [200] investigated L-fuzzy-rough set theory from an axiomatic method Zhao etal [201] suggested the new concept based on fuzzy variableprecision rough sets for handling the noise of perturbationand misclassification Wu et al [202] introduced a newattribute reduction approach focusing on the interval type2 fuzzy-rough set model and providing some properties ofinterval type 2 fuzzy-rough sets Yan et al [203] proposedgeneralising the rough set model with fuzzy relation on twouniverses using fuzzy theory and probabilistic methods Yangand Yao [204] investigated the multiagent DTRS model Xuet al [205] examined the GRS approach based on the roughmembership function Xia and Xu [206] investigated intu-itionistic fuzzy information changing Wu [207] examinedfuzzy-rough sets based on 119905-norms and discussed algebraicstructures and fuzzy topologies Feng et al [208] suggestedthe soft rough sets concept instead of equivalence classesand defined the parameterized soft set of upper and lowerapproximations Meng et al [209] suggested an approach forcalculating the upper and lower approximations for fuzzy softsets which efficiently define the boundary Li and Zhou [210]and Li et al [211] suggested a multiperspective explanationof the decision-theoretic rough set approach and attributereduction Jia et al [212] investigated the problem related toattribute reduction for decision-theoretic rough set theoryLiu et al [213] and Liu et al [214] explored multiple-categoryclassification with the DTRS method and applications inmanagement science Degang et al [215] introduced a novelapproach to examine fuzzy-rough sets by integrating gran-ular computing Hu et al [94] used kernel functions forintroducing the fuzzy similarity relations and developed thegreedy algorithm based on dimensionality reduction Maand Sun [216] proposed a probabilistic rough set model ontwo universes Ma and Sun [217] investigated the decision-theoretic rough set theory over two universes based on theidea of classical DTRS theory Liu et al [218] studied the GRSapproach based on twouniverses and discussed its propertiesChen et al [102] used fuzzy-rough sets to present a matrix

of fuzzy discernibility Zhang et al [111] proposed a generalframework of intuitionistic fuzzy-rough sets and discussedthe intuitionistic fuzzy operator and the properties of themodel with the dual domain caseWei et al [219] investigatedthe relationships among rough approximations of fuzzy-rough setmodels Chen et al [117] explored the interpretationof several types of membership functions geometricallyby using the lower approximations in fuzzy-rough sets interms of square distances in Krein spaces Ma and Hu [220]examined lattice structures and the topology of L-fuzzy-rough sets by considering upper and lower approximationssets Yang et al [70] suggested a fuzzy probabilistic roughset model on two universes Liang et al [59] examinedinformation retrieval and filtering by employing the DTRStheory Zhang and Miao [221] and Zhang and Miao [222]proposed the double-quantitative approximation space forpresenting two double-quantitative rough set theories Yaoet al [101] suggested the variable precision (120579 120590)-fuzzy-rough sets theory regarding fuzzy granules Liu et al [223]investigated logistic regression for classification based ondecision-theoretic rough sets theory Ma et al [224] sug-gested a decision region distribution preservation reductionin decision-theoretic rough set theory Qian et al [225]investigated the multigranulation decision-theoretic roughset approach Sun et al [82] examined the DTRFS applicationandmodel Zhang andMiao [226] constructed a fundamentalreduction framework for two-category decision-theoreticrough sets Gong and Zhang [105] investigated a method ofintuitionistic fuzzy sets and variable precision rough sets toconstruct an extended intuitionistic fuzzy-rough set modelZhao and Xiao [131] defined the general type-2 fuzzy-roughsets and discussed the basic properties of lower and upperapproximation operators Zhang and Miao [227] and Zhangand Miao [228] examined attribute reduction for proposingrough set theory models Drsquoeer et al [118] investigatedthe drawbacks and benefits of implicatorndashconjunctor-basednoise-tolerant fuzzy-rough set models Li and Cui [77]studied the characterizations of the topology of fuzzy-roughsets by considering the similarity of fuzzy relations Li andCui [229] investigated fuzzy topologies considering a lowerfuzzy-rough approximation operator based on the t-conormXu et al [230] introduced a knowledge reduction approach ina generalised approximation space over two universes Li and

6 Complexity

Xu [231] introduced the multigranulation decision-theoreticrough set approach in the ordered information systemLiang et al [232] suggested three-way decisions by extendingthe DTRS approach to a qualitative environment Ju et al[233] presented a moderate attribute reduction model inDTRS Li and Xu [234] investigated the double-quantitativeDTRS approach based on assembling the upper and lowerapproximations of the GRS and DTRS methods Wang [114]examined type 2 fuzzy-rough sets by considering two finiteuniverses and utilising axiomatic and constructive methodsand investigated some topological properties of type 2 fuzzy-rough sets Zhang and Min [235] used three-way decisionsregarding recommender systems Wang [114] defined anupper approximation number for developing a quantitativeanalysis of covering-based rough set theory Wang et al [25]proposed a fitting fuzzy-rough set model to conduct featureselection Yang and Hu [178] proposed a definition of fuzzy120573-covering approximation spaces by introducing some newdefinitions of fuzzy 120573-covering approximation spaces Marsquosfuzzy covering-based rough set and the properties of fuzzy120573-covering approximation spaces Wang [29] investigatedcharacterizations of generalised fuzzy-rough sets in the corerough equalities context Namburu et al [32] suggested a softfuzzy-rough set-based segmentation of magnetic resonancebrain image for handling the uncertainty regarding the indis-cernibility and vagueness in a parameterized representationWang [30] examined the topological structures of L-fuzzy-rough set theory Liang et al [232] examined triangular fuzzydecision-theoretic rough sets Zhang andYao [236] examinedfunctions of the Gini objective for three-way classificationSun et al [237] explored three-way group decision-making byusing multigranulation fuzzy decision-theoretic rough setsFeng et al [34] investigated reduction of themultigranulationfuzzy information system based on uncertainty measuresby considering variable precision multigranulation decision-theoretic fuzzy-rough set theory and avoiding the changingof negative region and positive region to small ones Sun etal [62] proposed the new fuzzy-rough set on a probabilisticapproximation space and used it with respect to decision-making in unconventional emergency management Hu etal [171] proposed a new incremental method to updateapproximations of fuzzy information system over two uni-verses Fan et al [72] introduced several double-quantitativeDTRS (DQ-DTRFS) models based on logical conjunctionand disjunction operations Qiao and Hu [238] proposed agranular variable precision L-fuzzy-rough set theory basedon residuated lattices with arbitrary L-fuzzy relations Lianget al [172] examined the decision principles of three-waydecision rules based on the variation of loss functions withIFSs

4 Research Method

For the research methodology in this study we used thePreferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) provided byMoher et al [239] PRISMAhas two main parts including systematic reviews and meta-analyses Systematic reviews provide objective summaries ofwhat has been written and found out about research topics

This is especially valuable in wide research areas wheremany publications exist each focusing on a narrow aspectof the field [240] Systematic reviews aim to provide a fulloverview of research conducted in a specific area until thepresent date All research procedures have to bemade explicitbefore the actual behaviour of the review to make the processobjective and replicable Meta-analysis provides a meansof mathematically integrating findings employing diversestatistical approaches to study the diversity of the articlesIn this kind of synthesis original studies that are compatiblewith their quality level are selected This aspect may help andhighlight different facts which individual primary studies failto do for example it may prove that results are statisticallysignificant and relevant when small primary studies provideinconclusive and uncertain results with a large confidenceinterval [241] The main goal of PRISMA is to help theresearchers and practitioners complete a comprehensive andclear literature review [242]

Several previous studies have been conducted usingPRISMA in the various fields to develop a comprehensiveliterature review [242ndash244] In order to implement thePRISMA method in this study we accomplish three mainsteps including literature search choosing the eligible pub-lished papers and extraction of data and summarising [237]

41 Literature Search In this step we have chosen the Webof Science database to provide a comprehensive applicationof fuzzy-rough set theories The literature search was accom-plished based on two keywords including rough set theoriesand fuzzy-rough set theories We attempted to collect thecurrent published papers from 2010 to 2016 In the first stepof our search we found 5648 scholarly papers related tothe rough set theories and fuzzy-rough set theories whichwere extracted according to our strategy search In the nextstep we searched to find the papers which were publishedbetween 2010 and 2016 and checked the duplicate paperswith redundant information After this step 296 papers wereremaining After removing 17 records due to duplicationwe screened papers based on the titles and abstracts andirrelevant papers were removed In total 193 potentiallyrelated papers remained (see Figure 3)

42 Articles Eligibility In this step of the review for thepurpose of eligibility we reviewed the full text of each articleindependently (which extracted from the last step) In thelast step we carefully identified the related articles to attaina consensus Book chapters unpublished working paperseditorial notes master dissertations and doctoral thesestextbooks and non-English papers were excluded In the endwe selected 132 articles related to the fuzzy-rough sets from28 international scholarly journals between 2010 and 2016whichmet our inclusion criteriaWe selected the papers from2010 because of such a large number of papers published inthis field

43 Data Extraction and Summarising In the final step ofour methodology after negotiation with other authors somerequired information was collected and finally 132 articleswere reviewed and summarised In Table 1 all the selected

Complexity 7

Scre

enin

gIn

clude

dEl

igib

ility

Search in Web of Science for rough sets theories (n = 4856)

Search in Web of Science for fuzzy-rough sets theories (n = 792)

Search in databases for fuzzy-rough sets from 2010 to 2016 (n = 296)

Removed records due to duplicates (n = 17)

Screened records based of abstract review (n = 279)

Excluded records based of abstract review (n = 86)

Assessed full-text articles for eligibility (n = 193)

Excluded full-text articles with reasons (n = 71)

Studies included in qualitative synthesis (n = 122)

Identified papers in references (n = 10)

Included articles for meta-analysis (n = 132)

Iden

tifica

tion

Figure 3 Study flowchart for the identification screening eligibility and inclusion of articles

Table 1 Classification of papers based on application area

Application areas Frequency Percentage of frequencyInformation systems 12 909Decision-making 9 833Approximation operators 15 1136Feature and attribute selection 24 2045Fuzzy set theories 37 2727Other application areas 35 2348Total 132 10000

articles were classified into different classifications includinginformation systems decision-making approximate reason-ing feature and attribute selection machine learning fuzzyset theories and other application areas Also the articleswere summarised and reviewed based on the various criteriasuch as author and year of publication author nationalitiesapplication field type of study study category study contri-bution and journal in which they appeared We believe thatreviewing summarising and classifying the articles helped us

to achieve some critical and valuable insights Consequentlysome suggestions and recommendations for future studieswere proposed Furthermore we believe that this reviewpaper was accomplished very carefully and it presented acomprehensive source regarding the fuzzy-rough set theoriesIt should be noted that the main difficulty of using thePRISMA method was to understand what methodologieswere used from the abstract and the research section of theselected articles Thus we required going through the full

8 Complexity

content of articles and took a more detailed look to evaluatethe exactly applied approach to evaluate the fuzzy-roughsets Although a considerable amount of time was spent inthe selection process it helped us choose the most suitablepublications in conducting the review

5 Application Areas Classification

Although categorising and combining the articles in the fieldsof fuzzy-rough sets is complex for the classification taskwe used the opinions of experts Consequently based onopinions of experts we categorised articles into six differentapplications areas (see Table 1) In the following section allselected articles were summarised and reviewed based on thevarious criteria

51 Distribution Papers Based on Information Systems Roughset theory is a powerful and popular machine learningmethod It is particularly appropriate for dealing with theinformation systems that exhibit inconsistencies Fuzzy settheory integrated with the rough set theory detects degreesof inconsistency in the data Xu et al [245] examined a newparallel attribute reduction algorithm by focusing on fuzzy-rough set theory and mutual information rather than calcu-lating of the fuzzy-rough lower and upper approximationsexplicitlyMoreover Yang et al [246] investigated some roughsets models for handling big data but this study does notfocus on explicitly calculating the upper and lower approx-imations Some previous scholars investigated the parallelmodels for computing the upper and lower approximationsin the traditional rough set model For example Zhang etal [247] introduced a new MapReduce-based approach forcalculating the upper and lower approximations in a decisionsystem Zhang et al [248] used different approximationsto compare knowledge acquisition Yang and Chen [249]suggested a novel approach to calculate the positive regionsuch as the union of the lower approximation of all classesDubois and Prade [250] explored the relationship similar-ities and differences between twofold fuzzy sets and roughsets Ouyang et al [50] defined new fuzzy rough sets whichgeneralized the concept of fuzzy rough sets in the senseof Radzikowska and Kerre [28] and that of Mi and Zhang[186] Kuznetsov et al [251] introduced an approach basedon the fuzzy-rough sets which were called the (119868 119869)-fuzzy-rough set Zeng et al [52] developed a new Hybrid Distance(HD) in Hybrid Information System (HIS) based on thevalue difference metric and a new fuzzy-rough approachwas designed by integrating the Gaussian kernel and HDdistance Feng and Mi [39] investigated variable precisionmultigranulation fuzzy decision-theoretic rough sets in aninformation system Chen et al [55] introduced a newapproach to build a polygonal rough-fuzzy set and presenteda novel fuzzy interpolative reasoning approach for sparsefuzzy rule-based systems based on the ratio of fuzziness of theconstructed polygonal rough-fuzzy sets Table 2 representssignificant distribution findings of information systems basedon the author and year of publication application field typeof study study category and study contribution The results

represented in this table indicate that 12 articles have beenpublished in the area of information systems

52 Distribution Papers Based on Decision-Making Whilethere are a variety of existing methods for various applicationareas from imprecise data the fuzzy-rough set method hasan advantage for decision-making for large volumes of datasince it focuses on reducing the number of attributes requiredto characterize a concept without losing essential informationrequired for decision-making Although rough sets have sev-eral advantages over other methods they generate a numberof rules creating difficulties in decision-making [252] Afuzzy-rough set is a data mining algorithm for decision-making based on incomplete inconsistent imprecise andvague data Fuzzy-rough set theory is an extension of thefuzzy conventional set theory that supports approximationsin decision-making However rough set theories are valu-able mathematical approaches for explaining and showinginsufficient and incomplete information and also have beenextensively used in numerous application areas such ascomprehensive evaluation and uncertainty decision-makingwith fuzzy information [62] Greco et al [253] proposed anew dominance rough set framework that is appropriate forpreference analysis [31 254ndash261] This study investigated thedecision-making problem with multicriteria and attributeswhere dominance relations are extracted from similarity rela-tions andmulticriteria are created from equivalence relationsand numerical attributes are created from nominal attributesAn extensive review of multicriteria decision analysis basedon dominance rough sets is given in Greco et al [253]Dominance rough sets have also been applied to ordinalattribute reduction [253 262] and multicriteria classification[263ndash266] Recently several previous studies extended thefuzzy set based on the dominance rough set approach[106 170 258 267 268] Hu et al [60] proposed a novelapproach for extracting the fuzzy preference relations byusing a fuzzy-rough set model Liang and Liu [61] presenteda naive approach of intuitionistic fuzzy decision-theoreticrough sets (IFDTRSs) and analysed its related properties Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets The detailed results of this section are presented inTable 3 The findings represented in this table indicate that 8articles have been published in the area of decision-making

53 Distribution Papers Based on Approximation OperatorsA rough set approximates a crisp set by two other sets thatgive a lower and upper approximation of the crisp set Inthe rough set analysis the data is expected to be discrete Inenormous information systems the computation of the lowerand upper approximation sets is a demanding process bothregarding processing time and memory utilisation A roughset approximates a certain set of elements with two othersubsets called upper and lower approximations Through thefuzzy-rough lower and upper approximation fuzzy-rough settheory can model the quality or typicality of instances withintheir respective classes and hence it is an ideal tool to detectborder points and noisy instances The lower approximation

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Journal of

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Complexity 5

A

U

(a) The lower approximation

s

A

U

(b) The upper approximation

Figure 2 The concept 119860 is approximated by means of the lower and upper approximations [41 42]

and upper approximations by using the similarity betweentwo objects Hu et al [197] proposed a novel fuzzy-roughset model based on which a straightforward and efficienthybrid attribute reduction algorithm was designed Lingraset al [198] and Lingras et al [199] applied the DTRS theoryfor clustering analysis She and Wang [200] investigated L-fuzzy-rough set theory from an axiomatic method Zhao etal [201] suggested the new concept based on fuzzy variableprecision rough sets for handling the noise of perturbationand misclassification Wu et al [202] introduced a newattribute reduction approach focusing on the interval type2 fuzzy-rough set model and providing some properties ofinterval type 2 fuzzy-rough sets Yan et al [203] proposedgeneralising the rough set model with fuzzy relation on twouniverses using fuzzy theory and probabilistic methods Yangand Yao [204] investigated the multiagent DTRS model Xuet al [205] examined the GRS approach based on the roughmembership function Xia and Xu [206] investigated intu-itionistic fuzzy information changing Wu [207] examinedfuzzy-rough sets based on 119905-norms and discussed algebraicstructures and fuzzy topologies Feng et al [208] suggestedthe soft rough sets concept instead of equivalence classesand defined the parameterized soft set of upper and lowerapproximations Meng et al [209] suggested an approach forcalculating the upper and lower approximations for fuzzy softsets which efficiently define the boundary Li and Zhou [210]and Li et al [211] suggested a multiperspective explanationof the decision-theoretic rough set approach and attributereduction Jia et al [212] investigated the problem related toattribute reduction for decision-theoretic rough set theoryLiu et al [213] and Liu et al [214] explored multiple-categoryclassification with the DTRS method and applications inmanagement science Degang et al [215] introduced a novelapproach to examine fuzzy-rough sets by integrating gran-ular computing Hu et al [94] used kernel functions forintroducing the fuzzy similarity relations and developed thegreedy algorithm based on dimensionality reduction Maand Sun [216] proposed a probabilistic rough set model ontwo universes Ma and Sun [217] investigated the decision-theoretic rough set theory over two universes based on theidea of classical DTRS theory Liu et al [218] studied the GRSapproach based on twouniverses and discussed its propertiesChen et al [102] used fuzzy-rough sets to present a matrix

of fuzzy discernibility Zhang et al [111] proposed a generalframework of intuitionistic fuzzy-rough sets and discussedthe intuitionistic fuzzy operator and the properties of themodel with the dual domain caseWei et al [219] investigatedthe relationships among rough approximations of fuzzy-rough setmodels Chen et al [117] explored the interpretationof several types of membership functions geometricallyby using the lower approximations in fuzzy-rough sets interms of square distances in Krein spaces Ma and Hu [220]examined lattice structures and the topology of L-fuzzy-rough sets by considering upper and lower approximationssets Yang et al [70] suggested a fuzzy probabilistic roughset model on two universes Liang et al [59] examinedinformation retrieval and filtering by employing the DTRStheory Zhang and Miao [221] and Zhang and Miao [222]proposed the double-quantitative approximation space forpresenting two double-quantitative rough set theories Yaoet al [101] suggested the variable precision (120579 120590)-fuzzy-rough sets theory regarding fuzzy granules Liu et al [223]investigated logistic regression for classification based ondecision-theoretic rough sets theory Ma et al [224] sug-gested a decision region distribution preservation reductionin decision-theoretic rough set theory Qian et al [225]investigated the multigranulation decision-theoretic roughset approach Sun et al [82] examined the DTRFS applicationandmodel Zhang andMiao [226] constructed a fundamentalreduction framework for two-category decision-theoreticrough sets Gong and Zhang [105] investigated a method ofintuitionistic fuzzy sets and variable precision rough sets toconstruct an extended intuitionistic fuzzy-rough set modelZhao and Xiao [131] defined the general type-2 fuzzy-roughsets and discussed the basic properties of lower and upperapproximation operators Zhang and Miao [227] and Zhangand Miao [228] examined attribute reduction for proposingrough set theory models Drsquoeer et al [118] investigatedthe drawbacks and benefits of implicatorndashconjunctor-basednoise-tolerant fuzzy-rough set models Li and Cui [77]studied the characterizations of the topology of fuzzy-roughsets by considering the similarity of fuzzy relations Li andCui [229] investigated fuzzy topologies considering a lowerfuzzy-rough approximation operator based on the t-conormXu et al [230] introduced a knowledge reduction approach ina generalised approximation space over two universes Li and

6 Complexity

Xu [231] introduced the multigranulation decision-theoreticrough set approach in the ordered information systemLiang et al [232] suggested three-way decisions by extendingthe DTRS approach to a qualitative environment Ju et al[233] presented a moderate attribute reduction model inDTRS Li and Xu [234] investigated the double-quantitativeDTRS approach based on assembling the upper and lowerapproximations of the GRS and DTRS methods Wang [114]examined type 2 fuzzy-rough sets by considering two finiteuniverses and utilising axiomatic and constructive methodsand investigated some topological properties of type 2 fuzzy-rough sets Zhang and Min [235] used three-way decisionsregarding recommender systems Wang [114] defined anupper approximation number for developing a quantitativeanalysis of covering-based rough set theory Wang et al [25]proposed a fitting fuzzy-rough set model to conduct featureselection Yang and Hu [178] proposed a definition of fuzzy120573-covering approximation spaces by introducing some newdefinitions of fuzzy 120573-covering approximation spaces Marsquosfuzzy covering-based rough set and the properties of fuzzy120573-covering approximation spaces Wang [29] investigatedcharacterizations of generalised fuzzy-rough sets in the corerough equalities context Namburu et al [32] suggested a softfuzzy-rough set-based segmentation of magnetic resonancebrain image for handling the uncertainty regarding the indis-cernibility and vagueness in a parameterized representationWang [30] examined the topological structures of L-fuzzy-rough set theory Liang et al [232] examined triangular fuzzydecision-theoretic rough sets Zhang andYao [236] examinedfunctions of the Gini objective for three-way classificationSun et al [237] explored three-way group decision-making byusing multigranulation fuzzy decision-theoretic rough setsFeng et al [34] investigated reduction of themultigranulationfuzzy information system based on uncertainty measuresby considering variable precision multigranulation decision-theoretic fuzzy-rough set theory and avoiding the changingof negative region and positive region to small ones Sun etal [62] proposed the new fuzzy-rough set on a probabilisticapproximation space and used it with respect to decision-making in unconventional emergency management Hu etal [171] proposed a new incremental method to updateapproximations of fuzzy information system over two uni-verses Fan et al [72] introduced several double-quantitativeDTRS (DQ-DTRFS) models based on logical conjunctionand disjunction operations Qiao and Hu [238] proposed agranular variable precision L-fuzzy-rough set theory basedon residuated lattices with arbitrary L-fuzzy relations Lianget al [172] examined the decision principles of three-waydecision rules based on the variation of loss functions withIFSs

4 Research Method

For the research methodology in this study we used thePreferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) provided byMoher et al [239] PRISMAhas two main parts including systematic reviews and meta-analyses Systematic reviews provide objective summaries ofwhat has been written and found out about research topics

This is especially valuable in wide research areas wheremany publications exist each focusing on a narrow aspectof the field [240] Systematic reviews aim to provide a fulloverview of research conducted in a specific area until thepresent date All research procedures have to bemade explicitbefore the actual behaviour of the review to make the processobjective and replicable Meta-analysis provides a meansof mathematically integrating findings employing diversestatistical approaches to study the diversity of the articlesIn this kind of synthesis original studies that are compatiblewith their quality level are selected This aspect may help andhighlight different facts which individual primary studies failto do for example it may prove that results are statisticallysignificant and relevant when small primary studies provideinconclusive and uncertain results with a large confidenceinterval [241] The main goal of PRISMA is to help theresearchers and practitioners complete a comprehensive andclear literature review [242]

Several previous studies have been conducted usingPRISMA in the various fields to develop a comprehensiveliterature review [242ndash244] In order to implement thePRISMA method in this study we accomplish three mainsteps including literature search choosing the eligible pub-lished papers and extraction of data and summarising [237]

41 Literature Search In this step we have chosen the Webof Science database to provide a comprehensive applicationof fuzzy-rough set theories The literature search was accom-plished based on two keywords including rough set theoriesand fuzzy-rough set theories We attempted to collect thecurrent published papers from 2010 to 2016 In the first stepof our search we found 5648 scholarly papers related tothe rough set theories and fuzzy-rough set theories whichwere extracted according to our strategy search In the nextstep we searched to find the papers which were publishedbetween 2010 and 2016 and checked the duplicate paperswith redundant information After this step 296 papers wereremaining After removing 17 records due to duplicationwe screened papers based on the titles and abstracts andirrelevant papers were removed In total 193 potentiallyrelated papers remained (see Figure 3)

42 Articles Eligibility In this step of the review for thepurpose of eligibility we reviewed the full text of each articleindependently (which extracted from the last step) In thelast step we carefully identified the related articles to attaina consensus Book chapters unpublished working paperseditorial notes master dissertations and doctoral thesestextbooks and non-English papers were excluded In the endwe selected 132 articles related to the fuzzy-rough sets from28 international scholarly journals between 2010 and 2016whichmet our inclusion criteriaWe selected the papers from2010 because of such a large number of papers published inthis field

43 Data Extraction and Summarising In the final step ofour methodology after negotiation with other authors somerequired information was collected and finally 132 articleswere reviewed and summarised In Table 1 all the selected

Complexity 7

Scre

enin

gIn

clude

dEl

igib

ility

Search in Web of Science for rough sets theories (n = 4856)

Search in Web of Science for fuzzy-rough sets theories (n = 792)

Search in databases for fuzzy-rough sets from 2010 to 2016 (n = 296)

Removed records due to duplicates (n = 17)

Screened records based of abstract review (n = 279)

Excluded records based of abstract review (n = 86)

Assessed full-text articles for eligibility (n = 193)

Excluded full-text articles with reasons (n = 71)

Studies included in qualitative synthesis (n = 122)

Identified papers in references (n = 10)

Included articles for meta-analysis (n = 132)

Iden

tifica

tion

Figure 3 Study flowchart for the identification screening eligibility and inclusion of articles

Table 1 Classification of papers based on application area

Application areas Frequency Percentage of frequencyInformation systems 12 909Decision-making 9 833Approximation operators 15 1136Feature and attribute selection 24 2045Fuzzy set theories 37 2727Other application areas 35 2348Total 132 10000

articles were classified into different classifications includinginformation systems decision-making approximate reason-ing feature and attribute selection machine learning fuzzyset theories and other application areas Also the articleswere summarised and reviewed based on the various criteriasuch as author and year of publication author nationalitiesapplication field type of study study category study contri-bution and journal in which they appeared We believe thatreviewing summarising and classifying the articles helped us

to achieve some critical and valuable insights Consequentlysome suggestions and recommendations for future studieswere proposed Furthermore we believe that this reviewpaper was accomplished very carefully and it presented acomprehensive source regarding the fuzzy-rough set theoriesIt should be noted that the main difficulty of using thePRISMA method was to understand what methodologieswere used from the abstract and the research section of theselected articles Thus we required going through the full

8 Complexity

content of articles and took a more detailed look to evaluatethe exactly applied approach to evaluate the fuzzy-roughsets Although a considerable amount of time was spent inthe selection process it helped us choose the most suitablepublications in conducting the review

5 Application Areas Classification

Although categorising and combining the articles in the fieldsof fuzzy-rough sets is complex for the classification taskwe used the opinions of experts Consequently based onopinions of experts we categorised articles into six differentapplications areas (see Table 1) In the following section allselected articles were summarised and reviewed based on thevarious criteria

51 Distribution Papers Based on Information Systems Roughset theory is a powerful and popular machine learningmethod It is particularly appropriate for dealing with theinformation systems that exhibit inconsistencies Fuzzy settheory integrated with the rough set theory detects degreesof inconsistency in the data Xu et al [245] examined a newparallel attribute reduction algorithm by focusing on fuzzy-rough set theory and mutual information rather than calcu-lating of the fuzzy-rough lower and upper approximationsexplicitlyMoreover Yang et al [246] investigated some roughsets models for handling big data but this study does notfocus on explicitly calculating the upper and lower approx-imations Some previous scholars investigated the parallelmodels for computing the upper and lower approximationsin the traditional rough set model For example Zhang etal [247] introduced a new MapReduce-based approach forcalculating the upper and lower approximations in a decisionsystem Zhang et al [248] used different approximationsto compare knowledge acquisition Yang and Chen [249]suggested a novel approach to calculate the positive regionsuch as the union of the lower approximation of all classesDubois and Prade [250] explored the relationship similar-ities and differences between twofold fuzzy sets and roughsets Ouyang et al [50] defined new fuzzy rough sets whichgeneralized the concept of fuzzy rough sets in the senseof Radzikowska and Kerre [28] and that of Mi and Zhang[186] Kuznetsov et al [251] introduced an approach basedon the fuzzy-rough sets which were called the (119868 119869)-fuzzy-rough set Zeng et al [52] developed a new Hybrid Distance(HD) in Hybrid Information System (HIS) based on thevalue difference metric and a new fuzzy-rough approachwas designed by integrating the Gaussian kernel and HDdistance Feng and Mi [39] investigated variable precisionmultigranulation fuzzy decision-theoretic rough sets in aninformation system Chen et al [55] introduced a newapproach to build a polygonal rough-fuzzy set and presenteda novel fuzzy interpolative reasoning approach for sparsefuzzy rule-based systems based on the ratio of fuzziness of theconstructed polygonal rough-fuzzy sets Table 2 representssignificant distribution findings of information systems basedon the author and year of publication application field typeof study study category and study contribution The results

represented in this table indicate that 12 articles have beenpublished in the area of information systems

52 Distribution Papers Based on Decision-Making Whilethere are a variety of existing methods for various applicationareas from imprecise data the fuzzy-rough set method hasan advantage for decision-making for large volumes of datasince it focuses on reducing the number of attributes requiredto characterize a concept without losing essential informationrequired for decision-making Although rough sets have sev-eral advantages over other methods they generate a numberof rules creating difficulties in decision-making [252] Afuzzy-rough set is a data mining algorithm for decision-making based on incomplete inconsistent imprecise andvague data Fuzzy-rough set theory is an extension of thefuzzy conventional set theory that supports approximationsin decision-making However rough set theories are valu-able mathematical approaches for explaining and showinginsufficient and incomplete information and also have beenextensively used in numerous application areas such ascomprehensive evaluation and uncertainty decision-makingwith fuzzy information [62] Greco et al [253] proposed anew dominance rough set framework that is appropriate forpreference analysis [31 254ndash261] This study investigated thedecision-making problem with multicriteria and attributeswhere dominance relations are extracted from similarity rela-tions andmulticriteria are created from equivalence relationsand numerical attributes are created from nominal attributesAn extensive review of multicriteria decision analysis basedon dominance rough sets is given in Greco et al [253]Dominance rough sets have also been applied to ordinalattribute reduction [253 262] and multicriteria classification[263ndash266] Recently several previous studies extended thefuzzy set based on the dominance rough set approach[106 170 258 267 268] Hu et al [60] proposed a novelapproach for extracting the fuzzy preference relations byusing a fuzzy-rough set model Liang and Liu [61] presenteda naive approach of intuitionistic fuzzy decision-theoreticrough sets (IFDTRSs) and analysed its related properties Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets The detailed results of this section are presented inTable 3 The findings represented in this table indicate that 8articles have been published in the area of decision-making

53 Distribution Papers Based on Approximation OperatorsA rough set approximates a crisp set by two other sets thatgive a lower and upper approximation of the crisp set Inthe rough set analysis the data is expected to be discrete Inenormous information systems the computation of the lowerand upper approximation sets is a demanding process bothregarding processing time and memory utilisation A roughset approximates a certain set of elements with two othersubsets called upper and lower approximations Through thefuzzy-rough lower and upper approximation fuzzy-rough settheory can model the quality or typicality of instances withintheir respective classes and hence it is an ideal tool to detectborder points and noisy instances The lower approximation

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Journal of

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Complexity

Xu [231] introduced the multigranulation decision-theoreticrough set approach in the ordered information systemLiang et al [232] suggested three-way decisions by extendingthe DTRS approach to a qualitative environment Ju et al[233] presented a moderate attribute reduction model inDTRS Li and Xu [234] investigated the double-quantitativeDTRS approach based on assembling the upper and lowerapproximations of the GRS and DTRS methods Wang [114]examined type 2 fuzzy-rough sets by considering two finiteuniverses and utilising axiomatic and constructive methodsand investigated some topological properties of type 2 fuzzy-rough sets Zhang and Min [235] used three-way decisionsregarding recommender systems Wang [114] defined anupper approximation number for developing a quantitativeanalysis of covering-based rough set theory Wang et al [25]proposed a fitting fuzzy-rough set model to conduct featureselection Yang and Hu [178] proposed a definition of fuzzy120573-covering approximation spaces by introducing some newdefinitions of fuzzy 120573-covering approximation spaces Marsquosfuzzy covering-based rough set and the properties of fuzzy120573-covering approximation spaces Wang [29] investigatedcharacterizations of generalised fuzzy-rough sets in the corerough equalities context Namburu et al [32] suggested a softfuzzy-rough set-based segmentation of magnetic resonancebrain image for handling the uncertainty regarding the indis-cernibility and vagueness in a parameterized representationWang [30] examined the topological structures of L-fuzzy-rough set theory Liang et al [232] examined triangular fuzzydecision-theoretic rough sets Zhang andYao [236] examinedfunctions of the Gini objective for three-way classificationSun et al [237] explored three-way group decision-making byusing multigranulation fuzzy decision-theoretic rough setsFeng et al [34] investigated reduction of themultigranulationfuzzy information system based on uncertainty measuresby considering variable precision multigranulation decision-theoretic fuzzy-rough set theory and avoiding the changingof negative region and positive region to small ones Sun etal [62] proposed the new fuzzy-rough set on a probabilisticapproximation space and used it with respect to decision-making in unconventional emergency management Hu etal [171] proposed a new incremental method to updateapproximations of fuzzy information system over two uni-verses Fan et al [72] introduced several double-quantitativeDTRS (DQ-DTRFS) models based on logical conjunctionand disjunction operations Qiao and Hu [238] proposed agranular variable precision L-fuzzy-rough set theory basedon residuated lattices with arbitrary L-fuzzy relations Lianget al [172] examined the decision principles of three-waydecision rules based on the variation of loss functions withIFSs

4 Research Method

For the research methodology in this study we used thePreferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) provided byMoher et al [239] PRISMAhas two main parts including systematic reviews and meta-analyses Systematic reviews provide objective summaries ofwhat has been written and found out about research topics

This is especially valuable in wide research areas wheremany publications exist each focusing on a narrow aspectof the field [240] Systematic reviews aim to provide a fulloverview of research conducted in a specific area until thepresent date All research procedures have to bemade explicitbefore the actual behaviour of the review to make the processobjective and replicable Meta-analysis provides a meansof mathematically integrating findings employing diversestatistical approaches to study the diversity of the articlesIn this kind of synthesis original studies that are compatiblewith their quality level are selected This aspect may help andhighlight different facts which individual primary studies failto do for example it may prove that results are statisticallysignificant and relevant when small primary studies provideinconclusive and uncertain results with a large confidenceinterval [241] The main goal of PRISMA is to help theresearchers and practitioners complete a comprehensive andclear literature review [242]

Several previous studies have been conducted usingPRISMA in the various fields to develop a comprehensiveliterature review [242ndash244] In order to implement thePRISMA method in this study we accomplish three mainsteps including literature search choosing the eligible pub-lished papers and extraction of data and summarising [237]

41 Literature Search In this step we have chosen the Webof Science database to provide a comprehensive applicationof fuzzy-rough set theories The literature search was accom-plished based on two keywords including rough set theoriesand fuzzy-rough set theories We attempted to collect thecurrent published papers from 2010 to 2016 In the first stepof our search we found 5648 scholarly papers related tothe rough set theories and fuzzy-rough set theories whichwere extracted according to our strategy search In the nextstep we searched to find the papers which were publishedbetween 2010 and 2016 and checked the duplicate paperswith redundant information After this step 296 papers wereremaining After removing 17 records due to duplicationwe screened papers based on the titles and abstracts andirrelevant papers were removed In total 193 potentiallyrelated papers remained (see Figure 3)

42 Articles Eligibility In this step of the review for thepurpose of eligibility we reviewed the full text of each articleindependently (which extracted from the last step) In thelast step we carefully identified the related articles to attaina consensus Book chapters unpublished working paperseditorial notes master dissertations and doctoral thesestextbooks and non-English papers were excluded In the endwe selected 132 articles related to the fuzzy-rough sets from28 international scholarly journals between 2010 and 2016whichmet our inclusion criteriaWe selected the papers from2010 because of such a large number of papers published inthis field

43 Data Extraction and Summarising In the final step ofour methodology after negotiation with other authors somerequired information was collected and finally 132 articleswere reviewed and summarised In Table 1 all the selected

Complexity 7

Scre

enin

gIn

clude

dEl

igib

ility

Search in Web of Science for rough sets theories (n = 4856)

Search in Web of Science for fuzzy-rough sets theories (n = 792)

Search in databases for fuzzy-rough sets from 2010 to 2016 (n = 296)

Removed records due to duplicates (n = 17)

Screened records based of abstract review (n = 279)

Excluded records based of abstract review (n = 86)

Assessed full-text articles for eligibility (n = 193)

Excluded full-text articles with reasons (n = 71)

Studies included in qualitative synthesis (n = 122)

Identified papers in references (n = 10)

Included articles for meta-analysis (n = 132)

Iden

tifica

tion

Figure 3 Study flowchart for the identification screening eligibility and inclusion of articles

Table 1 Classification of papers based on application area

Application areas Frequency Percentage of frequencyInformation systems 12 909Decision-making 9 833Approximation operators 15 1136Feature and attribute selection 24 2045Fuzzy set theories 37 2727Other application areas 35 2348Total 132 10000

articles were classified into different classifications includinginformation systems decision-making approximate reason-ing feature and attribute selection machine learning fuzzyset theories and other application areas Also the articleswere summarised and reviewed based on the various criteriasuch as author and year of publication author nationalitiesapplication field type of study study category study contri-bution and journal in which they appeared We believe thatreviewing summarising and classifying the articles helped us

to achieve some critical and valuable insights Consequentlysome suggestions and recommendations for future studieswere proposed Furthermore we believe that this reviewpaper was accomplished very carefully and it presented acomprehensive source regarding the fuzzy-rough set theoriesIt should be noted that the main difficulty of using thePRISMA method was to understand what methodologieswere used from the abstract and the research section of theselected articles Thus we required going through the full

8 Complexity

content of articles and took a more detailed look to evaluatethe exactly applied approach to evaluate the fuzzy-roughsets Although a considerable amount of time was spent inthe selection process it helped us choose the most suitablepublications in conducting the review

5 Application Areas Classification

Although categorising and combining the articles in the fieldsof fuzzy-rough sets is complex for the classification taskwe used the opinions of experts Consequently based onopinions of experts we categorised articles into six differentapplications areas (see Table 1) In the following section allselected articles were summarised and reviewed based on thevarious criteria

51 Distribution Papers Based on Information Systems Roughset theory is a powerful and popular machine learningmethod It is particularly appropriate for dealing with theinformation systems that exhibit inconsistencies Fuzzy settheory integrated with the rough set theory detects degreesof inconsistency in the data Xu et al [245] examined a newparallel attribute reduction algorithm by focusing on fuzzy-rough set theory and mutual information rather than calcu-lating of the fuzzy-rough lower and upper approximationsexplicitlyMoreover Yang et al [246] investigated some roughsets models for handling big data but this study does notfocus on explicitly calculating the upper and lower approx-imations Some previous scholars investigated the parallelmodels for computing the upper and lower approximationsin the traditional rough set model For example Zhang etal [247] introduced a new MapReduce-based approach forcalculating the upper and lower approximations in a decisionsystem Zhang et al [248] used different approximationsto compare knowledge acquisition Yang and Chen [249]suggested a novel approach to calculate the positive regionsuch as the union of the lower approximation of all classesDubois and Prade [250] explored the relationship similar-ities and differences between twofold fuzzy sets and roughsets Ouyang et al [50] defined new fuzzy rough sets whichgeneralized the concept of fuzzy rough sets in the senseof Radzikowska and Kerre [28] and that of Mi and Zhang[186] Kuznetsov et al [251] introduced an approach basedon the fuzzy-rough sets which were called the (119868 119869)-fuzzy-rough set Zeng et al [52] developed a new Hybrid Distance(HD) in Hybrid Information System (HIS) based on thevalue difference metric and a new fuzzy-rough approachwas designed by integrating the Gaussian kernel and HDdistance Feng and Mi [39] investigated variable precisionmultigranulation fuzzy decision-theoretic rough sets in aninformation system Chen et al [55] introduced a newapproach to build a polygonal rough-fuzzy set and presenteda novel fuzzy interpolative reasoning approach for sparsefuzzy rule-based systems based on the ratio of fuzziness of theconstructed polygonal rough-fuzzy sets Table 2 representssignificant distribution findings of information systems basedon the author and year of publication application field typeof study study category and study contribution The results

represented in this table indicate that 12 articles have beenpublished in the area of information systems

52 Distribution Papers Based on Decision-Making Whilethere are a variety of existing methods for various applicationareas from imprecise data the fuzzy-rough set method hasan advantage for decision-making for large volumes of datasince it focuses on reducing the number of attributes requiredto characterize a concept without losing essential informationrequired for decision-making Although rough sets have sev-eral advantages over other methods they generate a numberof rules creating difficulties in decision-making [252] Afuzzy-rough set is a data mining algorithm for decision-making based on incomplete inconsistent imprecise andvague data Fuzzy-rough set theory is an extension of thefuzzy conventional set theory that supports approximationsin decision-making However rough set theories are valu-able mathematical approaches for explaining and showinginsufficient and incomplete information and also have beenextensively used in numerous application areas such ascomprehensive evaluation and uncertainty decision-makingwith fuzzy information [62] Greco et al [253] proposed anew dominance rough set framework that is appropriate forpreference analysis [31 254ndash261] This study investigated thedecision-making problem with multicriteria and attributeswhere dominance relations are extracted from similarity rela-tions andmulticriteria are created from equivalence relationsand numerical attributes are created from nominal attributesAn extensive review of multicriteria decision analysis basedon dominance rough sets is given in Greco et al [253]Dominance rough sets have also been applied to ordinalattribute reduction [253 262] and multicriteria classification[263ndash266] Recently several previous studies extended thefuzzy set based on the dominance rough set approach[106 170 258 267 268] Hu et al [60] proposed a novelapproach for extracting the fuzzy preference relations byusing a fuzzy-rough set model Liang and Liu [61] presenteda naive approach of intuitionistic fuzzy decision-theoreticrough sets (IFDTRSs) and analysed its related properties Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets The detailed results of this section are presented inTable 3 The findings represented in this table indicate that 8articles have been published in the area of decision-making

53 Distribution Papers Based on Approximation OperatorsA rough set approximates a crisp set by two other sets thatgive a lower and upper approximation of the crisp set Inthe rough set analysis the data is expected to be discrete Inenormous information systems the computation of the lowerand upper approximation sets is a demanding process bothregarding processing time and memory utilisation A roughset approximates a certain set of elements with two othersubsets called upper and lower approximations Through thefuzzy-rough lower and upper approximation fuzzy-rough settheory can model the quality or typicality of instances withintheir respective classes and hence it is an ideal tool to detectborder points and noisy instances The lower approximation

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Complexity 7

Scre

enin

gIn

clude

dEl

igib

ility

Search in Web of Science for rough sets theories (n = 4856)

Search in Web of Science for fuzzy-rough sets theories (n = 792)

Search in databases for fuzzy-rough sets from 2010 to 2016 (n = 296)

Removed records due to duplicates (n = 17)

Screened records based of abstract review (n = 279)

Excluded records based of abstract review (n = 86)

Assessed full-text articles for eligibility (n = 193)

Excluded full-text articles with reasons (n = 71)

Studies included in qualitative synthesis (n = 122)

Identified papers in references (n = 10)

Included articles for meta-analysis (n = 132)

Iden

tifica

tion

Figure 3 Study flowchart for the identification screening eligibility and inclusion of articles

Table 1 Classification of papers based on application area

Application areas Frequency Percentage of frequencyInformation systems 12 909Decision-making 9 833Approximation operators 15 1136Feature and attribute selection 24 2045Fuzzy set theories 37 2727Other application areas 35 2348Total 132 10000

articles were classified into different classifications includinginformation systems decision-making approximate reason-ing feature and attribute selection machine learning fuzzyset theories and other application areas Also the articleswere summarised and reviewed based on the various criteriasuch as author and year of publication author nationalitiesapplication field type of study study category study contri-bution and journal in which they appeared We believe thatreviewing summarising and classifying the articles helped us

to achieve some critical and valuable insights Consequentlysome suggestions and recommendations for future studieswere proposed Furthermore we believe that this reviewpaper was accomplished very carefully and it presented acomprehensive source regarding the fuzzy-rough set theoriesIt should be noted that the main difficulty of using thePRISMA method was to understand what methodologieswere used from the abstract and the research section of theselected articles Thus we required going through the full

8 Complexity

content of articles and took a more detailed look to evaluatethe exactly applied approach to evaluate the fuzzy-roughsets Although a considerable amount of time was spent inthe selection process it helped us choose the most suitablepublications in conducting the review

5 Application Areas Classification

Although categorising and combining the articles in the fieldsof fuzzy-rough sets is complex for the classification taskwe used the opinions of experts Consequently based onopinions of experts we categorised articles into six differentapplications areas (see Table 1) In the following section allselected articles were summarised and reviewed based on thevarious criteria

51 Distribution Papers Based on Information Systems Roughset theory is a powerful and popular machine learningmethod It is particularly appropriate for dealing with theinformation systems that exhibit inconsistencies Fuzzy settheory integrated with the rough set theory detects degreesof inconsistency in the data Xu et al [245] examined a newparallel attribute reduction algorithm by focusing on fuzzy-rough set theory and mutual information rather than calcu-lating of the fuzzy-rough lower and upper approximationsexplicitlyMoreover Yang et al [246] investigated some roughsets models for handling big data but this study does notfocus on explicitly calculating the upper and lower approx-imations Some previous scholars investigated the parallelmodels for computing the upper and lower approximationsin the traditional rough set model For example Zhang etal [247] introduced a new MapReduce-based approach forcalculating the upper and lower approximations in a decisionsystem Zhang et al [248] used different approximationsto compare knowledge acquisition Yang and Chen [249]suggested a novel approach to calculate the positive regionsuch as the union of the lower approximation of all classesDubois and Prade [250] explored the relationship similar-ities and differences between twofold fuzzy sets and roughsets Ouyang et al [50] defined new fuzzy rough sets whichgeneralized the concept of fuzzy rough sets in the senseof Radzikowska and Kerre [28] and that of Mi and Zhang[186] Kuznetsov et al [251] introduced an approach basedon the fuzzy-rough sets which were called the (119868 119869)-fuzzy-rough set Zeng et al [52] developed a new Hybrid Distance(HD) in Hybrid Information System (HIS) based on thevalue difference metric and a new fuzzy-rough approachwas designed by integrating the Gaussian kernel and HDdistance Feng and Mi [39] investigated variable precisionmultigranulation fuzzy decision-theoretic rough sets in aninformation system Chen et al [55] introduced a newapproach to build a polygonal rough-fuzzy set and presenteda novel fuzzy interpolative reasoning approach for sparsefuzzy rule-based systems based on the ratio of fuzziness of theconstructed polygonal rough-fuzzy sets Table 2 representssignificant distribution findings of information systems basedon the author and year of publication application field typeof study study category and study contribution The results

represented in this table indicate that 12 articles have beenpublished in the area of information systems

52 Distribution Papers Based on Decision-Making Whilethere are a variety of existing methods for various applicationareas from imprecise data the fuzzy-rough set method hasan advantage for decision-making for large volumes of datasince it focuses on reducing the number of attributes requiredto characterize a concept without losing essential informationrequired for decision-making Although rough sets have sev-eral advantages over other methods they generate a numberof rules creating difficulties in decision-making [252] Afuzzy-rough set is a data mining algorithm for decision-making based on incomplete inconsistent imprecise andvague data Fuzzy-rough set theory is an extension of thefuzzy conventional set theory that supports approximationsin decision-making However rough set theories are valu-able mathematical approaches for explaining and showinginsufficient and incomplete information and also have beenextensively used in numerous application areas such ascomprehensive evaluation and uncertainty decision-makingwith fuzzy information [62] Greco et al [253] proposed anew dominance rough set framework that is appropriate forpreference analysis [31 254ndash261] This study investigated thedecision-making problem with multicriteria and attributeswhere dominance relations are extracted from similarity rela-tions andmulticriteria are created from equivalence relationsand numerical attributes are created from nominal attributesAn extensive review of multicriteria decision analysis basedon dominance rough sets is given in Greco et al [253]Dominance rough sets have also been applied to ordinalattribute reduction [253 262] and multicriteria classification[263ndash266] Recently several previous studies extended thefuzzy set based on the dominance rough set approach[106 170 258 267 268] Hu et al [60] proposed a novelapproach for extracting the fuzzy preference relations byusing a fuzzy-rough set model Liang and Liu [61] presenteda naive approach of intuitionistic fuzzy decision-theoreticrough sets (IFDTRSs) and analysed its related properties Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets The detailed results of this section are presented inTable 3 The findings represented in this table indicate that 8articles have been published in the area of decision-making

53 Distribution Papers Based on Approximation OperatorsA rough set approximates a crisp set by two other sets thatgive a lower and upper approximation of the crisp set Inthe rough set analysis the data is expected to be discrete Inenormous information systems the computation of the lowerand upper approximation sets is a demanding process bothregarding processing time and memory utilisation A roughset approximates a certain set of elements with two othersubsets called upper and lower approximations Through thefuzzy-rough lower and upper approximation fuzzy-rough settheory can model the quality or typicality of instances withintheir respective classes and hence it is an ideal tool to detectborder points and noisy instances The lower approximation

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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8 Complexity

content of articles and took a more detailed look to evaluatethe exactly applied approach to evaluate the fuzzy-roughsets Although a considerable amount of time was spent inthe selection process it helped us choose the most suitablepublications in conducting the review

5 Application Areas Classification

Although categorising and combining the articles in the fieldsof fuzzy-rough sets is complex for the classification taskwe used the opinions of experts Consequently based onopinions of experts we categorised articles into six differentapplications areas (see Table 1) In the following section allselected articles were summarised and reviewed based on thevarious criteria

51 Distribution Papers Based on Information Systems Roughset theory is a powerful and popular machine learningmethod It is particularly appropriate for dealing with theinformation systems that exhibit inconsistencies Fuzzy settheory integrated with the rough set theory detects degreesof inconsistency in the data Xu et al [245] examined a newparallel attribute reduction algorithm by focusing on fuzzy-rough set theory and mutual information rather than calcu-lating of the fuzzy-rough lower and upper approximationsexplicitlyMoreover Yang et al [246] investigated some roughsets models for handling big data but this study does notfocus on explicitly calculating the upper and lower approx-imations Some previous scholars investigated the parallelmodels for computing the upper and lower approximationsin the traditional rough set model For example Zhang etal [247] introduced a new MapReduce-based approach forcalculating the upper and lower approximations in a decisionsystem Zhang et al [248] used different approximationsto compare knowledge acquisition Yang and Chen [249]suggested a novel approach to calculate the positive regionsuch as the union of the lower approximation of all classesDubois and Prade [250] explored the relationship similar-ities and differences between twofold fuzzy sets and roughsets Ouyang et al [50] defined new fuzzy rough sets whichgeneralized the concept of fuzzy rough sets in the senseof Radzikowska and Kerre [28] and that of Mi and Zhang[186] Kuznetsov et al [251] introduced an approach basedon the fuzzy-rough sets which were called the (119868 119869)-fuzzy-rough set Zeng et al [52] developed a new Hybrid Distance(HD) in Hybrid Information System (HIS) based on thevalue difference metric and a new fuzzy-rough approachwas designed by integrating the Gaussian kernel and HDdistance Feng and Mi [39] investigated variable precisionmultigranulation fuzzy decision-theoretic rough sets in aninformation system Chen et al [55] introduced a newapproach to build a polygonal rough-fuzzy set and presenteda novel fuzzy interpolative reasoning approach for sparsefuzzy rule-based systems based on the ratio of fuzziness of theconstructed polygonal rough-fuzzy sets Table 2 representssignificant distribution findings of information systems basedon the author and year of publication application field typeof study study category and study contribution The results

represented in this table indicate that 12 articles have beenpublished in the area of information systems

52 Distribution Papers Based on Decision-Making Whilethere are a variety of existing methods for various applicationareas from imprecise data the fuzzy-rough set method hasan advantage for decision-making for large volumes of datasince it focuses on reducing the number of attributes requiredto characterize a concept without losing essential informationrequired for decision-making Although rough sets have sev-eral advantages over other methods they generate a numberof rules creating difficulties in decision-making [252] Afuzzy-rough set is a data mining algorithm for decision-making based on incomplete inconsistent imprecise andvague data Fuzzy-rough set theory is an extension of thefuzzy conventional set theory that supports approximationsin decision-making However rough set theories are valu-able mathematical approaches for explaining and showinginsufficient and incomplete information and also have beenextensively used in numerous application areas such ascomprehensive evaluation and uncertainty decision-makingwith fuzzy information [62] Greco et al [253] proposed anew dominance rough set framework that is appropriate forpreference analysis [31 254ndash261] This study investigated thedecision-making problem with multicriteria and attributeswhere dominance relations are extracted from similarity rela-tions andmulticriteria are created from equivalence relationsand numerical attributes are created from nominal attributesAn extensive review of multicriteria decision analysis basedon dominance rough sets is given in Greco et al [253]Dominance rough sets have also been applied to ordinalattribute reduction [253 262] and multicriteria classification[263ndash266] Recently several previous studies extended thefuzzy set based on the dominance rough set approach[106 170 258 267 268] Hu et al [60] proposed a novelapproach for extracting the fuzzy preference relations byusing a fuzzy-rough set model Liang and Liu [61] presenteda naive approach of intuitionistic fuzzy decision-theoreticrough sets (IFDTRSs) and analysed its related properties Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets The detailed results of this section are presented inTable 3 The findings represented in this table indicate that 8articles have been published in the area of decision-making

53 Distribution Papers Based on Approximation OperatorsA rough set approximates a crisp set by two other sets thatgive a lower and upper approximation of the crisp set Inthe rough set analysis the data is expected to be discrete Inenormous information systems the computation of the lowerand upper approximation sets is a demanding process bothregarding processing time and memory utilisation A roughset approximates a certain set of elements with two othersubsets called upper and lower approximations Through thefuzzy-rough lower and upper approximation fuzzy-rough settheory can model the quality or typicality of instances withintheir respective classes and hence it is an ideal tool to detectborder points and noisy instances The lower approximation

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Complexity 9

Table2Distrib

utionpapersbasedon

theinformationsyste

msa

rea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

LiuandSai[48]

Inform

ationsyste

ms

Develo

ped

Fuzzya

ndroug

hsets

Disc

ussedinvertibleup

pera

ndlower

approxim

ation

andprovided

thes

ufficientand

necessarycond

ition

for

lowe

rand

uppera

pproximationfuzzy-roug

handroug

hsets

Zhang[49]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance

intuition

isticfuzzy-roug

hsetfor

usingauditin

gris

kjudgmentininform

ation

syste

msecurity

Ouyangetal[50]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Generalise

dtheR

adzikowskaa

ndKe

rrea

pproach

basedon

fuzzy-roug

hsetswhich

werec

alledthe

(119868119869)-

fuzzy-roug

hset

DaiandTian

[51]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Develo

pedthefuzzy

constructand

relationof

the

fuzzy-roug

happroach

forset-valuedinform

ation

syste

ms

Zeng

etal[52]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewHybrid

Distance

(HD)inHybrid

Inform

ationSyste

ms(HIS)b

ased

onthev

alue

differencem

etric

and

anew

fuzzy-roug

happroach

was

desig

nedby

integratingtheG

aussiankernelandHD

distance

ShabirandSh

aheen[53]

Inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Suggestedan

ovelfram

eworkforfuzzificationof

roug

hsetswhentheo

bjectsare120572

-indiscerniblethatis

indiscernibleu

pto

acertain

degree

120572

Feng

andMi[39]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Investigatedthev

ariablep

recisio

nmultig

ranu

latio

nfuzzydecisio

n-theoretic

roug

hsetsin

aninform

ation

syste

m

WuandZh

ang[54]

Rand

omfuzzy

inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducednewrand

omfuzzy-roug

hsetapp

roaches

basedon

fuzzylogico

peratorsandrand

omfuzzysets

Chen

etal[55]

Fuzzyrule-based

syste

ms

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewapproach

tobu

ildap

olygon

alroug

h-fuzzysetand

presenta

novelfuzzy

interpolative

reason

ingapproach

forsparsefuzzy

rule-based

syste

ms

basedon

ther

atio

offuzzinesso

fthe

constructed

polygonalrou

gh-fu

zzysets

Tsangetal[56]

Inform

ationsyste

ms

Develo

ped

Fuzzy-roug

hsets

Exam

ined

somep

ropertieso

fcom

mun

icationbetween

inform

ationsyste

msb

ased

onfuzzy-roug

hsetm

odels

Han

etal[57]

Decision

inform

ationsyste

mProp

osed

Fuzzy-roug

hsets

Intro

ducedthen

eworderrelationabou

tbipolar-valued

fuzzysets

Aggarwal[58]

Fuzzyprob

abilistic

inform

ationsyste

mDevelo

ped

Fuzzy-roug

hsets

Develo

pedprob

abilisticvaria

blep

recisio

nfuzzy-roug

hsets(P-VP-FR

S)

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Complexity

Table3Distrib

utionpapersbasedon

thed

ecision

-makingarea

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Liangetal[59]

Multip

leattribute

grou

pdecisio

n-making

(MAG

DM)

Develo

ped

Fuzzy-roug

hand

triang

ular

fuzzysets

Designedan

ewalgorithm

ford

eterminationof

thev

alueso

flosses

used

intriang

ular

fuzzydecisio

n-theoretic

roug

hsets(TFD

TRS)

Huetal[60]

Decision

-making

Prop

osed

Fuzzypreference

and

roug

hsets

Prop

osed

anovelapproach

fore

xtractingfuzzypreference

relations

byusingafuzzy-rou

ghsetm

odel

LiangandLiu[61]

Inform

ationsyste

ms

Prop

osed

Fuzzy-roug

hsets

Presentedan

aive

approach

ofIFDTR

Ssandanalysisof

itsrelated

prop

ertie

s

Sunetal[62]

Decision

-making

Prop

osed

Fuzzy-roug

hsetsand

emergencymaterial

demandpredictio

n

Usedfuzzy-roug

hsetsforsolving

prob

lemsinem

ergencymaterial

demandpredictio

n

Zhangetal[63]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Presentedac

ommon

decisio

nmakingmod

elbasedon

hesitant

fuzzyandroug

hsets

named

HFroug

hsets

Zhan

andZh

u[64]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Extend

edthen

ew119885-

softroug

hfuzzyof

hemiring

sbased

onthe

notio

nof

softroug

hsetsandroug

hfuzzysets

SunandMa[

65]

Decision

-making

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelconcepto

fsoft

fuzzy-roug

hsetsby

integrating

tradition

alfuzzy-roug

hsetsandfuzzysoftsets

Yang

etal[66]

MCD

MProp

osed

Fuzzy-roug

hsets

Intro

ducedthec

oncept

oftheu

nion

the

inverseo

fbipolar

approxim

ationspacesand

theintersection

Sunetal[67]

Decision

-making

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-rou

ghapproxim

ationconcepto

n119894

prob

abilisticapproxim

ationspaceo

vertwoun

iverses

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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Stochastic AnalysisInternational Journal of

Complexity 11

is the union of all cases that can be classified with certainty inone of the decision classes whereas the upper approximationis a description of the instances that possibly belong to one ofthe decision classes With the utilisation of rough set theoryin the feature selection process the vague concept can bemodelled by the approximation of a vagueness set by a pairof precise concepts called lower and upper approximationsThe lower approximation or positive region is the union ofall instances that can be classified with certainty in one ofthe decision values whereas the upper approximation is adescription of the instances that possibly belong to one of thedecision values [269 270] Some previous papers investigatedsome properties of fuzzy-rough approximation operators Huet al [60] proposed a novel approach for extracting the fuzzypreference relations by using a fuzzy-rough set model Zhanget al [63] presented a common decision-makingmodel basedon hesitant fuzzy and rough sets named HF rough sets Sunand Ma [65] introduced a novel concept of soft fuzzy-roughsets by integrating the traditional fuzzy-rough sets and fuzzysoft sets Table 4 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 15 articles have been published in the area ofapproximation operators

54 Distribution Papers Based on Feature or Attribute Selec-tion There are several other instances of information thatcan be derived from data but in this section we focus onclassification Formally given a dataset of instances describedby conditional features and a decision feature classifiers aimto predict the class of a new instance given its conditionalfeatures Most classifiers first build a model based on thedata and then feed the new instance to the model to predictits class For example Support Vector Machines (SVMs)[98 271ndash273] construct a function that models a separatingborder between the different classes in the data and thevalue of that function for the new instance then determinesto what class it most likely belongs Decision trees [274275] generate rules from the data following a tree structurethat predict the class of a new instance Zhu et al [276]introduced a novel attribute reduction criterion for choosinglowest attributes while keeping the best performance of thecorresponding learning algorithms to some extent Inbaraniet al [277] proposed a new feature selection approachbased on high dimensionality in the medical dataset Thisclassifier has no modelling phase A new instance is classifieddirectly by looking up the closest instances in the data andclassifying it to the class mostly occurring among thosenearest neighbors Before the data can be used to build theclassification model and to classify the new instances thedata needs to be preprocessed For example there can bemissing values [278ndash281] in the data that need to be imputedPreprocessing can also be used to speed up or improvethe classification process For example fuzzy-rough featureselection techniques select features such that themembershipdegrees of the instances to the fuzzy-rough positive regionare maximised [195] or instance selection techniques selectinstances with a high membership degree to the fuzzy-rough

positive region [195] Jensen et al [83] proposed a modelby using a rough set for solving the problems related tothe propositional satisfiability perspective Qian et al [84]proposed an approach based on dimensionality reductiontogether with sample reduction for a heuristic process offuzzy-rough feature selection Derrac et al [88] presenteda new hybrid algorithm for reduction of data using featureand instance selection Jensen and Mac Parthalain [89]introduced two novel diverse ways of using the attributeand neighborhood approximation step for solving problemsof complexity of the subset evaluation metric Maji andGarai [91] presented a new feature selection approach basedon fuzzy-rough sets by maximising the significance andrelevance of the selected features Zeng et al [52] developeda new Hybrid Distance (HD) in Hybrid Information System(HIS) based on the value difference metric and a new fuzzy-rough approach by integrating the Gaussian kernel and HDdistance Cornelis et al [95] introduced and extended a newrough set theory based on the multiadjoint fuzzy-rough setsfor calculating the lower and upper approximations Yao etal [101] introduced a new fuzzy-rough approach called thevariable precision (120579 120590) fuzzy-rough approach based on fuzzygranules Zhao et al [103] introduced a robust model fordimension reduction by using fuzzy-rough sets to achievethe possible parameters Chen and Yang [104] integrated therough set and fuzzy-rough set model for attribute reductionin decision systems with real and symbolic valued conditionattributes Table 5 provides valuable distribution findings ofapproximation operators based on the author and year ofpublication application field type of study study categoryand study contribution The results represented in this tableindicate that 23 articles have been published in the area of theattribute or attribute selection

55 Distribution of Papers Based on Fuzzy Set Theories Inrecent years several studies have examined how rough settheory can be extended using various types of fuzzy settheories [53 173 238 261 282] which extends traditionalset theory in the sense that instances can belong to a setto a certain degree between 0 and 1 Most studies havebeen conducted on fuzzy sets with fuzzy-rough sets [3681 116 125 141 283 284] mainly focusing on preservingthe predictive power of datasets with the least featurespossible Some preliminary researches have been done onusing fuzzy-rough set theory for instance selection [88] andits combination with fuzzy sets [120 285] Apart from usingfuzzy-rough set theory for preprocessing it has also beenused successfully to tackle classification problems directlyfor example in rule induction [157 170 286 287] decision-making [49 59 65 288] improving 119870-NN classification[87 289ndash293] interval-valued fuzzy sets [108 122 130133 294 295] enhancing decision trees [165 296 297]hesitant fuzzy sets [132 133 137 173 298] and boostingSVMs [11 98] [25 26 68 106] Huang et al [106] proposedDominance Intuitionistic Fuzzy Decision Tables (DIFDT)based on the fuzzy-rough set approach Zhang [109] pro-posed intuitionistic fuzzy-rough sets based on intuitionis-tic fuzzy coverings by using intuitionistic fuzzy triangu-lar norms and intuitionistic fuzzy implication operators

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Applied MathematicsJournal of

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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Mathematical PhysicsAdvances in

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Stochastic AnalysisInternational Journal of

12 Complexity

Table4Distrib

utionpapersbasedon

approxim

ationop

erators

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Fanetal[68]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

dominance-based

fuzzy-roug

hset

mod

elford

ecision

analysis

Cheng[69]

Approxim

ations

Prop

osed

Fuzzy-roug

hsets

Suggestedtwoincrem

entalapp

roachesfor

fast

compu

tingof

ther

ough

fuzzyapproxim

ationinclu

ding

cutsetso

ffuzzy

setsandbo

undary

sets

Yang

etal[70]

Approxim

ater

easoning

Prop

osed

Fuzzyprob

abilistic

roug

hsets

Suggestedan

ewfuzzyprob

abilisticroug

hsetapp

roach

Wuetal[71]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

happroxim

ation

Exam

ined

thep

roblem

relatedto

constructrou

ghapproxim

ations

ofav

ague

setinfuzzyapproxim

ation

space

Fanetal[72]

Approxim

ation

reason

ing

Prop

osed

Fuzzy-roug

hsetand

decisio

n-theoretic

roug

hsets

Prop

osed

theq

uantitativ

edecision

-theoretic

roug

hfuzzysetapp

roachesb

ased

onlogicald

isjun

ctionand

logicalcon

junctio

n

Sunetal[73]

Approxim

ater

easoning

Develop

edRo

ughsetand

fuzzy-roug

hsets

Prop

osed

theu

pper

andlower

approxim

ations

offuzzy

setsbasedon

ahybrid

indiscernibilityrelation

Estajietal[74]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthen

otionof

a120579-lo

wer

and120579-up

per

approxim

ations

ofafuzzy

subsetof

119871

LiandYin[75]

Approxim

ater

easoning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelfuzzyalgebraics

tructure

which

was

anam

edTL

-fuzzy-roug

hsemigroup

basedon

a119879-up

perfuzzy-rou

ghapproxim

ationand120599-lower

and

operators

Zhangetal[76]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Disc

ussedan

approxim

ationseto

favagues

etin

Pawlakrsquos

approxim

ationspace

LiandCu

i[77]

Approxim

ation

operators

Prop

osed

Fuzzy-roug

hsets

Intro

ducedandinvestigated

fuzzytopo

logies

indu

ced

byfuzzy-roug

happroxim

ationop

eratorsa

ndthe

concepto

fsim

ilarityof

fuzzyrelations

Wuetal[78]

Approxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Investigated

thea

xiom

aticcharacteriz

ations

ofrelatio

n-based(119878

119879)-f

uzzy-rou

ghapproxim

ation

operators

Hao

andLi

[79]

L-fuzzy-roug

happroxim

ationspace

Develo

ped

Fuzzy-roug

hsets

Disc

ussedther

elationshipbetween

119871-topo

logies

and

119871-fuzzy-roug

hsetsin

anarbitraryun

iverse

Cheng[80]

Approxim

ation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twoalgorithm

sbased

onforw

ardand

backwardapproxim

ations

which

werec

alledminer

ules

basedon

theb

ackw

ardapproxim

ationandminer

ules

basedon

theforwardapproxim

ation

Feng

etal[81]

Fuzzyapproxim

ation

operators

Develo

ped

Fuzzy-roug

hsets

Prop

osed

thea

pproximationof

asoft

setb

ased

ona

Pawlakapproxim

ationspace

Sunetal[82]

Prob

abilisticr

ough

fuzzy

set

Prop

osed

Fuzzy-roug

hsets

Intro

ducedap

robabilistic

roug

hfuzzysetu

singthe

cond

ition

alprob

abilityof

afuzzy

event

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Journal of

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Complexity 13

Table5Distrib

utionpapersbasedon

featureo

rattributes

election

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Jensen

etal[83]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

amod

elby

usingroug

hsetsforsolving

prob

lemsrela

tedto

thep

ropo

sitionalsatisfi

ability

perspective

Qianetal[84]

Features

election

Prop

osed

Fuzzy-roug

hfeatures

election

Prop

osed

anapproach

basedon

dimensio

nality

redu

ctiontogether

with

sampler

eductio

nfora

heuristicprocesso

ffuzzy-rou

ghfeatures

electio

n

Huetal[85]

Featuree

valuation

andselection

Develo

ped

Fuzzy-roug

hsets

Prop

osed

softfuzzy-roug

hsetsby

developing

roug

hsetsto

redu

cetheinfl

uenceo

fnoise

Hon

getal[86]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thelearningalgorithm

from

theincom

plete

quantitatived

atas

etsb

ased

onroug

hsets

Onan[87]

Machine

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewcla

ssificatio

napproach

basedon

the

fuzzy-roug

hnearestn

eighbo

rmetho

dforthe

selection

offuzzy-roug

hinstances

Derrace

tal[88]

Features

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewhybrid

algorithm

forreductio

nof

data

byusingfeaturea

ndinsta

nces

election

Jensen

andMac

Parthalain

[89]

Features

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtwono

veld

iverse

waysb

yusingan

attribute

andneighb

orho

odapproxim

ationste

pforsolving

prob

lemso

fcom

plexity

ofthes

ubsetevaluationmetric

Paletal[90]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forp

attern

classificatio

nbasedon

granular

compu

ting

Zhangetal[24]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetb

ased

oninform

ation

entro

pyforfeature

selection

Majiand

Garai[91]

Features

election

Develo

ped

Fuzzy-roug

hsets

Presentedan

ewfeatures

electionapproach

basedon

fuzzy-roug

hsetsby

maxim

izingsig

nificantand

relevanceo

fthe

selected

features

Ganivadae

tal[92]

Features

electio

nProp

osed

Fuzzy-roug

hsets

Prop

osed

theg

ranu

larn

euraln

etworkforrecognizing

salient

features

ofdatabased

onfuzzysetsanda

fuzzy-roug

hset

Wangetal[20]

Features

ubset

selection

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hsetapp

roachforfeature

subset

selection

Kumar

etal[93]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelalgorithm

basedon

fuzzy-roug

hsets

forfutures

electio

nandcla

ssificatio

nof

datasetswith

multifeatures

Huetal[94]

Features

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

twokind

sofk

ernelized

fuzzy-roug

hsetsby

integratingkernelfunctio

nsandfuzzy-roug

hset

approaches

Cornelis

etal[95]

Attributes

election

Develo

ped

Fuzzy-roug

hsets

Intro

ducedandextend

edan

ewroug

hsettheorybased

onmultia

djoint

fuzzy-roug

hsetsforc

alculatin

gthe

lower

andup

pera

pproximations

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

14 Complexity

Table5Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Mac

Parthalain

andJensen

[96]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Presentedvario

usseveralu

nsup

ervisedfeature

selection(FS)

approaches

basedon

fuzzy-roug

hsets

DaiandXu

[97]

Attributes

election

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thea

ttributes

electionmetho

dbasedon

fuzzy-roug

hsetsfortum

orcla

ssificatio

n

Chen

etal[98]

Supp

ortvector

machines(SV

Ms)

Develo

ped

Fuzzy-roug

hsets

Improved

theh

ardmarginsupp

ortvectorm

achines

basedon

fuzzy-roug

hsetsandatrainingmem

bership

sampleinthec

onstraints

Huetal[99]

Supp

ortvector

machine

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelapproach

fora

fuzzy-roug

hmod

elwhich

was

named

softfuzzy-roug

hsetsforrob

ust

classificatio

nbasedon

thea

pproach

Weietal[100]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtwokind

soffuzzy-rou

ghapproxim

ations

anddefin

edtwocorrespo

ndingrelativep

ositive

region

redu

cts

Yaoetal[101]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ewexpand

edfuzzy-roug

happroach

which

was

named

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghapproach

basedon

fuzzygranules

Chen

etal[102]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Develo

pedan

ewalgorithm

forfi

ndingredu

ctionbased

onthem

inim

alfactorsinthed

iscernibilitymatrix

Zhao

etal[103]

Attributer

eductio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedtherob

ustm

odelof

dimensio

nredu

ctionby

usingfuzzy-roug

hsetsfor(reflectingof

ther

educts)

achieved

onthep

ossib

leparameters

Chen

andYang

[104]

Attributer

eductio

nDevelo

ped

Fuzzy-roug

hsets

Integratingther

ough

setand

fuzzy-roug

hsetm

odelfor

attributer

eductio

nin

decisio

nsyste

msw

ithrealand

symbo

licvalued

cond

ition

attributes

Complexity 15

Zhang et al [111] examined intuitionistic fuzzy-rough setsbased on two universes general binary relations and anintuitionistic fuzzy implicator 119868 and a pair (119879 119868) of theintuitionistic fuzzy 119905-norm 119879 Huang et al [113] developeda novel multigranulation rough set which was named theIntuitionistic Fuzzy Multigranulation Rough Set (IFMGRS)Wang [114] examined type-2 fuzzy-rough sets based onextended 119905-norms and type 2 fuzzy relations in the convexnormal fuzzy truth values Chen et al [117] introduced ageometrical interpretation and application of this type ofmembership functionsMa [119] presented two novel types offuzzy covering rough set for bridges linking covering roughsets and fuzzy-rough theory Reference [29] investigatedthe topological characterizations of generalised fuzzy-roughregarding basic rough equalities He et al [120] proposedan inconsistent fuzzy decision system and reductions andimproved discernibility matrix-based algorithms to discoverreducts Bai et al [123] proposed an approach based on rough-fuzzy sets for the extraction of spatial fuzzy decision rulesfrom spatial data that simultaneously were of two kinds offuzziness roughness and uncertainties Zhao and Hu [124]examined the fuzzy and interval-valued Fuzzy ProbabilisticRough Sets within frameworks of fuzzy and interval-valuedfuzzy probabilistic approximation spaces Huang et al [125]introduced an Intuitionistic Fuzzy (IF) graded approximationspace based on IF graded neighborhood and discussedinformation entropy and rough entropy measures Li et al[299] integrated the interval type 2 fuzzy with rough settheory by using the axiomatic and constructive approachesKhuman et al [126] investigated the type 2 fuzzy sets andrough-fuzzy sets to provide a practical means to expresscomplex uncertainty without the associated difficulty of atype 2 fuzzy set Zhang [295] introduced a new modelbased on interval-valued rough intuitionistic fuzzy sets byintegrating the classical Pawlak rough set and interval-valuedIF set theory Hu [130] developed an integrative modelconsidering interval-valued fuzzy sets and variable precisionnamed generalised interval-valued fuzzy variable precisionrough sets Yang et al [132] investigated a novel fuzzy-roughset model based on constructive and axiomatic approachesto introduce the hesitant fuzzy-rough set model Zhang et al[133] integrated the interval-valued hesitant fuzzy sets withrough sets to introduce the novel model named the interval-valued hesitant fuzzy-rough set Tiwari and Srivastava [300]investigated the results of some previous studies regardingthe one-to-one correspondence between the family of fuzzypreorders on a nonempty set Chen et al [136] proposeda new rough-fuzzy approach for handling representationand utilisation of various levels of uncertainty in knowl-edge Table 6 provides valuable distribution results of fuzzysets theories based on the author and year of publicationapplication field type of study study category and studycontribution The results represented in this table indicatethat 37 articles have been published in the area of the attributeor attribute selection

56 Distribution of Papers Based on Other Application AreasIn recent decades rough sets and fuzzy-rough sets theorieshave been employed in various application areas such as

data mining [4 5 86 301ndash303] software packages [141304] web ontology [138 305ndash307] pattern recognition [24148 187 308ndash310] granular computing [38 221 238 251]genetic algorithm [310ndash313] prototype selection [145 163]solid transportation [146 314 315] social networks [316ndash318] artificial neural network [92 153 319] remote sens-ing [320 321] and gene selection [158 322ndash324] An etal [140] analysed a regression algorithm based on fuzzypartition fuzzy-rough sets estimation of regression valuesand fuzzy approximation for estimating wind speed Shirazet al [142] proposed a new fuzzy-rough DEA approachby combining the classical DEA rough set and fuzzyset theory to accommodate the uncertainty Zhou et al[144] developed a new approach for automatic selectionof the threshold parameter to determine the approxima-tion regions in rough set-based clustering Vluymans etal [19] introduced a novel kind of classifier for imbal-anced multi-instance data based on fuzzy-rough set theoryGanivada et al [150] proposed a Fuzzy-Rough GranularSelf-Organising Map (FRGSOM) by including the three-dimensional linguistic vector and connection weights forclustering the patterns which included overlapping regionsAmiri and Jensen [151] introduced three missing imputationapproaches based on the fuzzy-rough nearest neighborsnamely VQNNI OWANNI and FRNNI Feng and Mi [39]introduced the use of data mining approaches to forecastthe need of maintenance Affonso et al [153] proposed anew method for biological image classification by a rough-fuzzy artificial neural network Pahlavani et al [155] pro-posed a novel fuzzy-rough set model to extract the rulesin the ANFIS based classification procedure for choosingthe optimum features Zhao et al [157] developed a rule-based classifier fuzzy-rough using one generalised fuzzy-rough set model to introduce a novel idea which was calledconsistence degree Maji and Pal [158] presented a newfuzzy equivalence partition matrix for approximating thetrue marginal and joint distributions of continuous geneexpression values Huang and Kuo [159] investigated twoperspectives of cross-lingual semantic document similaritymeasures based on the fuzzy sets and rough sets which werenamed formulation of similarity measures and documentrepresentation Ramentol et al [161] developed a learningalgorithm for considering the imbalance representation andproposed a classification algorithm for imbalanced data byusing the fuzzy-rough sets and ordered weighted averageaggregation Derrac et al [163] introduced a new fuzzy-rough set model for prototype selection by optimising thebehaviour of this classifier Zhao et al [166] introduced anovel complement information entropymethod in the fuzzy-rough sets based on the arbitrary fuzzy relations inner-classand outer-class information Changdar et al [168] presenteda new genetic-ant colony optimisation algorithm in a fuzzy-rough set environment for solving problems related to thesolid multiple Travelling Salesmen Problem (mTSP) Sun andMa [169] introduced a novelmodel to evaluate the emergencyplants for unconventional emergency events using soft fuzzy-rough set theory The results of this section are provided inTable 7

16 Complexity

Table6Distrib

utionpapersbasedon

fuzzysettheories

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Gon

gandZh

ang[105]

Fuzzysyste

mProp

osed

Roug

hsets

Suggestedan

ovelextensionof

ther

ough

settheoryby

integratingprecision

roug

hsettheoryvaria

bles

and

intuition

isticfuzzy-roug

hsettheory

Huang

etal[106]

Intuition

isticfuzzy

Prop

osed

Roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

dominance

intuition

isticfuzzydecisio

ntables

(DIFDT)

basedon

afuzzy-rou

ghsetapp

roach

Pawlak[3]

Type

2fuzzy

Prop

osed

Intervaltype

2fuzzyandroug

hsets

Integrated

theintervaltype2

fuzzysetswith

roug

hset

theory

byusingthea

xiom

aticandconstructiv

eapproaches

Yang

andHinde

[107]

Fuzzyset

Prop

osed

Fuzzysetand

R-fuzzysets

Suggestedan

ewextensionof

fuzzysetswhich

was

called119877-fuzzysetsas

anelem

ento

frou

ghsets

Chengetal[108]

Interval-valuedfuzzy

Develo

ped

Interval-valued

fuzzy-roug

hsets

Prop

osed

twonewalgorithm

sbased

onconverse

and

positivea

pproximations

which

weren

amed

MRB

PAandMRB

CA

Zhang[109]

Intuition

istic

fuzzy

Prop

osed

Fuzzy-roug

hsetsand

intuition

istic

fuzzysets

Prop

osed

intuition

isticfuzzy-roug

hsetsbasedon

intuition

isticfuzzycoverin

gsusingintuition

isticfuzzy

triang

ular

norm

sand

intuition

isticfuzzyim

plication

operators

Xuee

tal[110]

Fuzzy-roug

hC-

means

cluste

ring

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsemisu

pervise

dou

tlier

detection(FRS

SOD)m

etho

dforh

elpingsome

fuzzy-roug

hC-

means

cluste

ringandlabelledsamples

Zhangetal[111]

Intuition

istic

fuzzy

Develo

ped

Intuition

istic

fuzzy-roug

hsets

Exam

ined

theintuitio

nisticfuzzy-roug

hsetsbasedon

twoun

iversesgeneralbinaryrelationsand

anintuition

isticfuzzyim

plicator

Iand

apair(

119879119868)

ofthe

intuition

isticfuzzy119905-n

orm

119879Weietal[112]

Fuzzyentro

pyDevelop

edFu

zzy-roug

hsets

Analyzedandevaluatedther

ough

nessof

arou

ghset

basedon

fuzzyentro

pymeasures

WangandHu[40]

119871-fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eneralise

d119871-fuzzy-roug

hsetfor

more

generalisationof

then

otionof

119871-fuzzy-roug

hset

Huang

etal[113]

Intuition

isticfuzzy

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ovelan

ewmultig

ranu

latio

nroug

hset

which

was

named

theintuitio

nisticfuzzy

multi-granulationroug

hset(IFMGRS

)

Wang[114]

Type

2fuzzysets

Develo

ped

Fuzzy-roug

hsets

Exam

ined

type

2fuzzy-roug

hsetsbasedon

extend

ed119905-n

ormsa

ndtype

2fuzzyrelations

inthec

onvex

norm

alfuzzytruthvalues

Yang

andHu[115]

Fuzzy120573-coverin

gDevelop

edF u

zzy-roug

hsets

Exam

ined

then

ewfuzzycoverin

g-basedroug

happroach

bydefin

ingthen

otionof

afuzzy

120573-minim

aldescrip

tion

Luetal[116]

Type

2fuzzy

Develo

ped

Fuzzy-roug

hsets

Definedtype

2fuzzy-roug

hsetsbasedon

awavy-slice

representatio

nof

type

2fuzzysets

Chen

etal[117

]Fu

zzysim

ilarityrelation

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheg

eometric

alinterpretatio

nand

applicationof

thistype

ofmem

bershipfunctio

ns

Complexity 17Ta

ble6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Drsquoeere

tal[118]

Fuzzyrelations

Review

edFu

zzy-roug

hsets

Assessed

them

ostimpo

rtantfuzzy-rou

ghapproaches

basedon

theliterature

WangandHu[38]

Fuzzygranules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thev

ariablep

recisio

n(120579

120590)-f

uzzy-rou

ghset

toremedythed

efectsof

preexistingfuzzy-roug

hset

approaches

Ma[

119]

Fuzzy120573-coverin

gDevelop

edFu

zzy-roug

hsets

Presentedtwono

velkinds

offuzzycoverin

groug

hset

approaches

forb

ridgeslinking

coverin

groug

hsetsand

fuzzy-roug

htheory

Wang[29]

Fuzzytopo

logy

Develop

edFu

zzy-roug

hsets

Investigated

thetop

ologicalcharacteriz

ations

ofgeneralised

fuzzy-roug

hsetsregardingbasic

roug

hequalities

Hee

tal[120]

Fuzzydecisio

nsyste

mProp

osed

Fuzzy-roug

hsets

Prop

osed

theincon

sistent

fuzzydecisio

nsyste

mand

redu

ctions

andim

proved

discernibilitymatrix

-based

algorithm

stodiscover

redu

cts

Yang

etal[121]

Bipo

larfuzzy

sets

Develo

ped

Fuzzy-roug

hsets

Generalized

thefuzzy-rou

ghapproach

basedon

two

different

universesintrodu

cedby

SunandMa

Zhang[122]

Intervaltype

2Prop

osed

Fuzzy-roug

hsets

Suggestedan

ewmod

elforintervaltype2

roug

hfuzzy

setsby

employingconstructiv

eand

axiomaticmetho

ds

Baietal[123]

Fuzzydecisio

nrules

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anapproach

basedon

roug

hfuzzysetsforthe

extractio

nof

spatialfuzzy

decisio

nrulesfrom

spatial

datathatsim

ultaneou

slyweretwokind

soffuzziness

roug

hnessandun

certainties

Zhao

andHu[124]

Interval-valuedfuzzy

prob

abilistic

Develo

ped

Fuzzy-roug

hsets

Exam

ined

thefuzzy

andinterval-valuedfuzzy

prob

abilisticr

ough

setswith

infram

eworks

offuzzyand

interval-valuedfuzzyprob

abilisticapproxim

ation

spaces

Huang

etal[125]

Intuition

istic

fuzzy-roug

hsets

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheintuitio

nisticfuzzy(IF)

graded

approxim

ationspaceb

ased

ontheIFgraded

neighb

orho

odanddiscussedinform

ationentro

pyand

roug

hentro

pymeasures

Khu

man

etal[126]

Type

2fuzzyset

Develop

edFu

zzy-roug

hsets

Investigated

thetype2

fuzzysetsandroug

hfuzzysets

toprovidea

practic

almeans

toexpressc

omplex

uncertaintywith

outthe

associated

difficulty

ofatype2

fuzzyset

LiuandLin[127]

Intuition

istic

fuzzy-roug

hProp

osed

Fuzzy-roug

hsets

Prop

osed

anew

intuition

isticfuzzy-roug

happroach

basedon

thec

onflictdistance

Sunetal[128]

Interval-valuedroug

hintuition

isticfuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fram

eworkbasedon

intuition

istic

fuzzy-roug

hsetswith

thec

onstructivea

pproach

Zhangetal[129]

Hesitant

fuzzy

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thec

ommon

mod

elbasedon

roug

hset

theory

anddu

alhesitantfuzzy

setsnamed

dualhesitant

fuzzy-roug

hsetsby

considerationof

constructiv

eand

axiomaticmod

els

Hu[130]

Interval-valuedfuzzy

Develo

ped

Fuzzy-roug

hsets

Generalized

toan

integrativem

odelbasedon

consideringinterval-valuedfuzzysetsandvaria

ble

precision

setsnamed

generalized

interval-valuedfuzzy

varia

blep

recisio

nroug

hsets

18 Complexity

Table6Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhao

andXiao

[131]

Generaltype

2fuzzysets

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anovelmod

elby

integratinggeneraltype2

fuzzysets

roug

hsets

andthe120572

-plane

representatio

nmetho

d

Yang

etal[132]

Hesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Investigated

anovelfuzzy-roug

hmod

elbasedon

constructiv

eand

axiomaticapproaches

tointro

duce

the

hesitantfuzzy-rou

ghsetm

odel

Zhangetal[133]

Interval-valuedhesitant

fuzzyset

Prop

osed

Fuzzy-roug

hsets

Integrated

interval-valuedhesitantfuzzy

setswith

roug

hsetsto

intro

duce

anovelmod

elnamed

the

interval-valuedhesitantfuzzy-rou

ghset

WangandHu[134]

Fuzzy-valued

operations

Develop

edFu

zzy-roug

hsets

Exam

ined

thefuzzy-valuedop

erations

andthelattic

estructures

ofthea

lgebra

offuzzyvalues

Zhao

andHu[36]

IVFprob

ability

Develop

edFu

zzy-roug

hsets

Exam

ined

thed

ecision

-theoretic

roug

hset(DTR

S)metho

dbasedon

fuzzyandinterval-valuedfuzzy(IVF)

prob

abilisticapproxim

ationspaces

Mitrae

tal[135]

Fuzzyclu

sterin

gDevelo

ped

Fuzzy-roug

hsets

Develo

pedshadow

edsetsby

combining

fuzzyand

roug

hclu

sterin

g

Chen

etal[136]

Fuzzyruleinterpolation

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

roug

hfuzzyapproach

forh

andling

representatio

nandutilisatio

nof

diverselevelso

fun

certaintyin

know

ledge

Complexity 19

6 Distribution of Reviewed Paper by Journals

Table 8 presents the results of analysing the articles based ondistribution of the journals The articles related to the fuzzy-rough set theory have been chosen from 28 different inter-national scholarly journals indexed in the Web of Sciencedatabases Selected articles published alongwith an extensivediversity of journals that focus on fuzzy-rough set theoryvalidate different scholarly journals willingness to publish inthis field By far the highest ranking journal is the journal ofInformation Sciences with 36 articles followed by the journalof Fuzzy sets and Systems with 17 papers Furthermore morethan 60 percent of the total papers (83 out of 132 papers)were concentrated in five journals which play dominantroles in field of rough-fuzzy set theory Additionally in otherrankings the Soft Computing journal had the third rankwith 11 publications followed by journal of Knowledge-BasedSystems and IEEE Transactions on Fuzzy Systems with 10articles Hence based on this result we can conclude thatthese selected journals can be considered as themain journalson the fuzzy-rough set theory as the more than 60 percent ofthe articles were published in these journals Table 8 presentsthe list of journals where the fuzzy-rough set theory has beenpublished

7 Distribution of Articlesby Year of Publication

In recent decades the application of fuzzy-rough set theoryhas increased dramatically in the literature A historicalgrowth of fuzzy-rough sets has existed for many years Afrequency analysis of the 132 articles based on the articlespublished for different years is shown in Figure 4 During2010ndash2012 the articles published on fuzzy-rough set theorywere at a steady rate with 15 11 and 15 articlesThe uptrend inpapers outputs is observed since the year 2012 until 2016 Fig-ure 4 presents relevant information based on the frequencyof distribution by the year of publication Accordingly it canbe indicated that nowadays researchers are highly interestedin conducting research on fuzzy-rough set theory and itcan be predicted that in coming years these numbers willincrease

8 Distribution of PapersBased on Nationality of Authors

This review paper attempted to show the difference amongthe countries related to the fuzzy-rough set theory Twokinds of principles were used for identifying the character-istics in selected articles including the information gaineddirectly from the papers or the nationality of the firstauthor Figure 5 shows that authors from 16 nationalities andcountries investigated the fuzzy-rough set theory Most ofthe published papers were from China with 86 publicationsfollowed by India United Kingdom and Spain with 13 6 and5 publications respectively Figure 5 shows the frequency ofother nationalities as well

020406080

100120140

Freq

uenc

y

2011 2012 2013 2014 2015 20162010Year of publication

Figure 4 Distribution of articles by year of publication

65

10 54 3

3 32 1

1

1

1

1

1

1

1

6

Authors nationality

China India UK Spain Taiwan IranBelgium Cuba France Finland Macau ChileTurkey Brazil Singapore Australia

Figure 5 Distribution of papers based on nationality of authors

9 Discussion

There are some challenges regarding various applicationareas of fuzzy-rough set theory that can be interesting fordiscussion and future studies For example in the case offuzzy 120573-covering approximation spaces there are varioustopics which need further research such as matroidal struc-tures datamining the generalisation of fuzzy covering-basedrough sets topological properties and data compressionwith homomorphism and communication by using fuzzycovering-based rough sets In the area of multigranulationfuzzy-rough set theory somemore investigations are neededFor example it is necessary to explore the primary theoryand characterizations of multigranulation fuzzy-rough setsover two universes as well as attribute reduction of themultigranulation fuzzy approximation space over two uni-verses In the field of fuzzy information system over TwoUniverses (ISTU) further study is necessary to enhancethe current incremental algorithms by integration with theparallelism technique to update rough approximations Moreinvestigations are required in the area of interval-valued hes-itant fuzzy multigranulation rough sets over two universesto study uncertainty measures topological structures andattribute reduction methods Also further investigations areneeded in the area of the Dominance-Based Fuzzy-Rough SetApproach (DFRSA) by improving the attribute reductionrule induction and object reduction In the field of fuzzy

20 ComplexityTa

ble7Distrib

utionpapersbasedon

othera

pplicationareas

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Zhangetal[137]

Patte

rnrecogn

ition

Develo

ped

Fuzzya

ndroug

hsets

Presentedan

ovelroug

hsetm

odelby

integrating

multig

ranu

lationroug

hsetsover

twoun

iversesa

ndinterval-valuedhesitantfuzzy

setswhich

iscalled

interval-valuedhesitantfuzzy

multig

ranu

lationroug

hsets

Bobillo

andStraccia[138]

Web

ontology

Prop

osed

Fuzzy-roug

hsets

Presentedas

olutionrelated

tofuzzyDLs

androug

hDLs

which

iscalledfuzzy-roug

hDL

Liu[139]

Axiom

aticapproaches

Develo

ped

Fuzzy-roug

hsets

Investigatedthefi

xedun

iversalset

119880whereunless

otherw

isesta

tedthec

ardinalityof

119880isinfin

ite

Anetal[140]

Fuzzy-roug

hregressio

nDevelo

ped

Fuzzy-roug

hsets

Analyzedther

egressionalgorithm

basedon

fuzzy

partition

fuzzy-rou

ghsets

estim

ationof

regressio

nvaluesand

fuzzyapproxim

ationfore

stim

atingwind

speed

Riza

etal[141]

Softw

arep

ackages

Develop

edFu

zzy-roug

hsets

Implem

entin

ganddeveloping

fuzzy-roug

hsettheory

androug

hsettheoryalgorithm

sinthe119877

package

Shira

zetal[14

2]Fu

zzy-roug

hDEA

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hDEA

approach

bycombining

thec

lassicalDEA

rou

ghsetandfuzzyset

theory

toaccommod

atefor

uncertainty

Salto

sand

Weber

[11]

Datam

ining

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewsoftclu

sterin

gmod

elbasedon

supp

ort

vector

cluste

ring

Zeng

etal[143]

Bigdata

Develo

ped

Fuzzy-roug

hsets

Analyzedthec

hang

ingmechanism

softhe

attribute

values

andfuzzye

quivalence

relations

infuzzy-roug

hsets

Zhou

etal[144]

Roug

hset-b

ased

cluste

ring

Develo

ped

Fuzzy-roug

hsets

Develo

pedan

ewapproach

fora

utom

aticselectionof

the

thresholdparameter

ford

eterminingthea

pproximation

region

sinroug

hset-b

ased

cluste

ring

Verbiestetal[145]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedthep

rototype

selectionmod

elbasedon

fuzzy-roug

hsets

Vluym

anse

tal[19]

Multi-insta

ncelearning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelkind

ofcla

ssifier

forimbalanced

multi-instance

databasedon

fuzzy-roug

hsettheory

Pram

aniketal[146]

Solid

transportatio

nDevelo

ped

Fuzzy-roug

hsets

Develop

edbiob

jectivefuzzy-rou

ghexpected

value

approaches

Liu[14

7]Binary

relatio

nDevelo

ped

Fuzzy-roug

hsets

Definedthec

oncept

ofas

olitary

setfor

anybinary

relatio

nfro

m119880to

119881Meher

[148]

Patte

rncla

ssificatio

nDevelop

edFu

zzy-roug

hsets

Develo

pedthen

ewroug

hfuzzypatte

rncla

ssificatio

napproach

bycombining

them

erits

offuzzya

ndroug

hsets

Kund

uandPal[149]

Socialnetworks

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

commun

itydetectionalgorithm

toidentifyfuzzy-roug

hcommun

ities

Ganivadae

tal[150]

Granu

larc

ompu

ting

Prop

osed

Fuzzy-roug

hsets

Prop

osed

thefuzzy-rou

ghgranular

self-organizing

map

(FRG

SOM)inclu

ding

thethree-dim

ensio

nallinguistic

vector

andconn

ectio

nweightsforc

luste

ringpatte

rns

having

overlap

ping

region

s

Amiri

andJensen

[151]

Miss

ingdataim

putatio

nProp

osed

Fuzzy-roug

hsets

I nt ro

ducedthreem

issingim

putatio

napproaches

based

onfuzzy-roug

hnearestn

eighbo

rsnam

elyV

QNNI

OWANNIand

FRNNI

Complexity 21Ta

ble7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Ramentoletal[152]

Fuzzy-roug

him

balanced

learning

Prop

osed

Fuzzy-roug

hsets

Intro

ducedtheu

seof

dataminingapproaches

inorderto

forecastthen

eedof

maintenance

Affo

nsoetal[153]

Artificialneuralnetwork

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

metho

dforb

iologicalimagec

lassificatio

nby

arou

gh-fu

zzyartifi

cialneuralnetwork

Shuk

laandKirid

ena[

154]

Dyn

amicsupp

lychain

Develop

edFu

zzy-roug

hsets

Develo

pedan

ewfram

eworkbasedon

fuzzy-roug

hsets

forc

onfig

uringsupp

lychainnetworks

Pahlavanietal[155]

RemoteS

ensin

gProp

osed

Fuzzy-roug

hsets

Prop

osed

anovelfuzzy-roug

hsetm

odelto

extractrules

intheA

NFISbasedcla

ssificatio

nprocedurefor

choo

singthe

optim

umfeatures

Xiea

ndHu[156]

Fuzzy-roug

hset

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelextend

edmod

elbasedon

threek

inds

offuzzy-roug

hsetsandtwoun

iverses

Zhao

etal[157]

Con

structin

gcla

ssifier

Develop

edFu

zzy-roug

hsets

Develo

pedar

ule-basedcla

ssifier

fuzzy-roug

husingon

egeneralized

fuzzy-roug

hmod

elto

intro

duce

anovelidea

which

was

calledconsistence

degree

Majiand

Pal[158]

Genes

election

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewfuzzyequivalencep

artitionmatrix

for

approxim

atingof

thetruem

arginaland

jointd

istrib

utions

ofcontinuo

usgene

expressio

nvalues

Huang

andKu

o[159]

Cross-lin

gual

Develop

edFu

zzy-roug

hsets

Investigatedtwoperspectives

ofcross-lin

gualsemantic

documentsim

ilaritymeasuresb

ased

onfuzzysetsand

roug

hsetswhich

was

named

form

ulationof

similarity

measuresa

nddo

cumentrepresentation

Wangetal[160]

Activ

elearning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

fuzzy-roug

hsetapp

roachforthe

samplersquos

inconsistency

betweendecisio

nlabelsandcond

ition

alfeatures

Ramentoletal[161]

Imbalanced

classificatio

nProp

osed

Fuzzy-roug

hsets

Develo

pedalearningalgorithm

forc

onsid

eringthe

imbalancer

epresentationandprop

osed

aclassificatio

nalgorithm

forimbalanced

databy

usingfuzzy-roug

hsets

andorderedweightedaveragea

ggregatio

n

Zhangetal[162]

Paralleld

isassem

bly

sequ

ence

planning

Prop

osed

Fuzzy-roug

hsets

Prop

osed

anew

paralleld

isassem

blysequ

ence

planning

basedon

fuzzy-roug

hsetsto

redu

cetim

ecom

plexity

Derrace

tal[163]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ewfuzzy-roug

hsetm

odelforp

rototype

selectionbasedon

optim

izingthe

behavior

ofthiscla

ssifier

Verbiestetal[164]

Prototypes

election

Prop

osed

Fuzzy-roug

hsets

Improved

TheS

yntheticMinority

Over-Sampling

Techniqu

e(SM

OTE

)tobalanceimbalanced

dataand

prop

osed

twoprototypes

electio

napproaches

basedon

fuzzy-roug

hsets

Zhai[165]

Fuzzydecisio

ntre

esProp

osed

Fuzzy-roug

hsets

Prop

osed

newexpand

edattributes

usingsig

nificance

offuzzycond

ition

alattributes

with

respecttofuzzydecisio

nattributes

Zhao

etal[166]

Uncertaintymeasure

Prop

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelcomplem

entinformationentro

pymetho

din

fuzzy-roug

hsetsbasedon

arbitraryfuzzy

relationsinn

er-classandou

ter-cla

ssinform

ation

Huetal[167]

Fuzzy-roug

hset

Develop

edFu

zzy-roug

hsets

Exam

ined

thep

ropertieso

fsom

eexistingfuzzy-roug

hsets

indealingwith

noisy

dataandprop

osed

vario

usrobu

stapproaches

22 Complexity

Table7Con

tinued

Author

andreference

Applicationfield

Type

ofstu

dyStud

ycategory

Stud

ycontrib

ution

Changdar

etal[168]

Geneticalgorithm

Prop

osed

Fuzzy-roug

hsets

Presentedan

ewgenetic-ant

colony

optim

ization

algorithm

inafuzzy-rou

ghsetenviro

nmentfor

solving

prob

lemsrela

tedto

thes

olid

multip

leTravellin

gSalesm

enProb

lem

(mTS

P)

SunandMa[

169]

Emergencyplans

evaluatio

nProp

osed

Fuzzy-roug

hsets

Intro

ducedan

ovelmod

elto

evaluateem

ergencyplans

foru

ncon

ventionalemergencyeventsusingsoft

fuzzy-roug

hsettheory

Complexity 23

Table 8 Distribution of papers based on the name of journals

Name of journals Frequently PercentageInformation Sciences 36 2727Fuzzy sets and Systems 15 1136Soft Computing 11 833Knowledge-Based Systems 10 758IEEE Transactions On Fuzzy Systems 10 758Pattern Recognition 6 455International Journal of General Systems 5 379Journal of Approximate Reasoning 5 379Expert Systems with Applications 5 379Applied Soft Computing 5 379Applied Mathematical Modelling 4 303Pattern Recognition Letters 2 152IEEE Transactions on Knowledge and Data Engineering 2 152Neurocomputing 2 152Artificial Intelligence Review 1 076Expert Systems 1 076Data amp Knowledge Engineering 1 076Neural Networks 1 076Mathematics and Computers in Simulation 1 076Fundamenta Informaticae 1 076Socio-Economic Planning Sciences 1 076Theoretical Computer Science 1 076Engineering Applications of Artificial Intelligence 1 076International Journal of Production Research 1 076International Journal of Remote Sensing 1 076The International Journal of Advanced Manufacturing Technology 1 076Kybernetes 1 076Mathematics and Computers in Simulation 1 076Total 132 10000

neighborhood rough sets further study is necessary regard-ing classification learning and reasoning with uncertaintyIn addition in the area of type 2 fuzzy-rough sets furtherinvestigations are required regarding attribute reductionrelated to granular type 2 fuzzy sets and various methodsof knowledge discovery in the complex fuzzy informationsystems Furthermore although some studies have investi-gated type-2 variable precisionmultigranulation fuzzy-roughsets future studies can focus on uncertainty and reductionmeasures of variable precision multigranulation fuzzy-roughsets Moreover although some scholars have examined FuzzyProbabilistic Rough Sets (FPRSs) and Interval-Valued FuzzyProbabilistic Rough Sets (IVF-PRSs) with models of IVFand fuzzy probabilistic approximation spaces there is stillneed to focus on characterizations of axiomatic methodsin FPRSs and IVF-PRSs models Although some previouspapers investigated Gaussian Kernel Fuzzy-Rough Sets (FRS)in Hybrid Information Systems (HIS) further studies arerequired regarding technologies of parallel computing forexample Map Reduce to optimise the increment updatingmodel There are also some papers regarding intuitionisticfuzzy-rough set model However more investigation is nec-essary to improve and construct the dominance intuitionistic

fuzzy variable precision rough sets theory models Althoughsome previous papers examined the DTRS approach in thearea of fuzzy and IVF probabilistic approximation spacesthere is a need for more studies to be conducted on thecircumstance of IVF sets In addition there are some worksrelated to IFDTRSs focusing on decision-theoretic roughsets nonetheless there is a need for more investigationson generalisation models based on the IFDTRSs Althoughsome previous researchers focused on the fuzzy topologiesinduced by the fuzzy-rough approximation operators furtherarticles are necessary for enhancing the generalised similarityof fuzzy relations based on the 119905-norms and complete resid-uated lattices Furthermore although papers were publishedregarding the Intuitionistic Fuzzy Multigranulation RoughSets (IFMGRS) further enhancements of these models arerequired by focusing on an interval-valued IF environment

10 Conclusion

This review paper presented a comprehensive overview ofrecent fuzzy generations of rough sets theory in variousapplications areas In total 132 papers were selected forsystematic review and meta-analysis in the period 2010ndash2016

24 Complexity

from popular international journals accessible in the Webof Science database We carefully selected and reviewed 132studies about the fuzzy-rough set theory based on the titleabstract introduction research methods and conclusionsThese selected papers were categorised into six applicationareas Also all papers were classified based on the authorand year of publication author nationalities application fieldtype of study study category study contribution and journalin which they appeared Some points on fuzzy-rough settheory were gained from this review articleThe vast majorityof reviewed articles were published between 2013 and 2016In total the papers were classified into six areas includ-ing information systems decision-making approximationoperators feature and attribute selection fuzzy set theoriesand other application areas Fuzzy set theory combined withrough set theory was the most important application areawith 37 papers Furthermore 28 international peer reviewedjournals were considered in the current review paper TheJournal of Information Systems had the first rank amongthe considered journals regarding publishing papers relatedto the fuzzy-rough set theory The articles published at thebeginning of 2017 (if any) have not been included in thepresent paper because of the limited reporting time Weattempted to use those published articles in other sectionsof our review paper such as related works and introductionsections However this present review can be developedfor the future studies Another limitation is that the datawas collected from journals while the examined documentsdid not include textbooks doctoral and masterrsquos thesesand unpublished papers on MCDM problems Althoughwe attempted to provide the comprehensive review basedon the current and old literature nevertheless as a rec-ommendation for future studies the data can be collectedfrom these sources and the obtained results can be com-pared with the data obtained and reported in this studyAnother limitation of this review was that all of the paperswere extracted from the journals written in English Hencescientific journals in other languages were not included inthe review However the researchers believe that this papercomprehensively reviewed most of the papers publishedin international journals In this paper we reviewed 132papers which recently studied generalised fuzzy-rough setstheory but attempted to include the comprehensive list ofpapers in other sections In addition we carefully selectedand summarised the available papers of several publishersin the Web of Science database However some relevantoutlets remained beyond the scope of the current studyTherefore future researchers will be able to review thosepapers which are not considered in the current reviewAnother limitation of the survey is that although the paperpresents various journals and conference publications thatrecently studied generalised fuzzy-rough set models it doesnot include any of this topic discussed in the publishedbooks

Conflicts of Interest

The authors declare no conflicts of interest regarding thepublication of the paper

References

[1] C-C Yeh D-J Chi andM-F Hsu ldquoA hybrid approach of DEArough set and support vector machines for business failurepredictionrdquo Expert Systems with Applications vol 37 no 2 pp1535ndash1541 2010

[2] F E H Tay and L Shen ldquoEconomic and financial predictionusing rough sets modelrdquo European Journal of OperationalResearch vol 141 no 3 pp 641ndash659 2002

[3] Z a Pawlak ldquoRough setsrdquo International Journal of Computerand Information Sciences vol 11 no 5 pp 341ndash356 1982

[4] J Zhang T Li andHChen ldquoComposite rough sets for dynamicdata miningrdquo Information Sciences An International Journalvol 257 pp 81ndash100 2014

[5] Y Huang T Li C Luo H Fujita and S-J Horng ldquoMatrix-based dynamic updating rough fuzzy approximations for dataminingrdquo Knowledge-Based Systems vol 119 pp 273ndash283 2017

[6] J Hu T Li C Luo H Fujita and Y Yang ldquoIncrementalfuzzy cluster ensemble learning based on rough set theoryrdquoKnowledge-Based Systems vol 132 pp 144ndash155 2017

[7] M Ye X Wu X Hu and D Hu ldquoAnonymizing classificationdata using rough set theoryrdquo Knowledge-Based Systems vol 43pp 82ndash94 2013

[8] I-K Park and G-S Choi ldquoRough set approach for clusteringcategorical data using information-theoretic dependency mea-surerdquo Information Systems vol 48 pp 289ndash295 2015

[9] F Shi S Sun and J Xu ldquoEmploying rough sets and associationrule mining in KANSEI knowledge extractionrdquo InformationSciences vol 196 pp 118ndash128 2012

[10] F Pacheco M Cerrada R-V Sanchez D Cabrera C Li and JValente de Oliveira ldquoAttribute clustering using rough set theoryfor feature selection in fault severity classification of rotatingmachineryrdquo Expert Systems with Applications vol 71 pp 69ndash862017

[11] R Saltos and R Weber ldquoA Rough-Fuzzy approach for SupportVector Clusteringrdquo Information Sciences vol 339 pp 353ndash3682016

[12] D Chen Y Yang and Z Dong ldquoAn incremental algorithm forattribute reduction with variable precision rough setsrdquo AppliedSoft Computing Journal vol 45 pp 129ndash149 2016

[13] E-S M El-Alfy and M A Alshammari ldquoTowards scalablerough set based attribute subset selection for intrusion detec-tion using parallel genetic algorithm inMapReducerdquo SimulationModelling Practice andTheory vol 64 pp 18ndash29 2015

[14] S Eskandari and M M Javidi ldquoOnline streaming featureselection using rough setsrdquo International Journal of ApproximateReasoning vol 69 pp 35ndash57 2016

[15] J G and H Inbarani H ldquoHybrid Tolerance Rough SetmdashFireflybased supervised feature selection for MRI brain tumor imageclassificationrdquoApplied Soft Computing Journal vol 46 pp 639ndash651 2016

[16] C Hu S Liu and X Huang ldquoDynamic updating approx-imations in multigranulation rough sets while refining orcoarsening attribute valuesrdquo Knowledge-Based Systems vol 130pp 62ndash73 2017

[17] H Li D Li Y Zhai S Wang and J Zhang ldquoA novel attributereduction approach for multi-label data based on rough settheoryrdquo Information Sciences vol 367-368 pp 827ndash847 2016

[18] M S Raza and U Qamar ldquoAn incremental dependencycalculation technique for feature selection using rough setsrdquoInformation Sciences An International Journal vol 343344 pp41ndash65 2016

Complexity 25

[19] S Vluymans D Sanchez Tarrago Y Saeys C Cornelis and FHerrera ldquoFuzzy rough classifiers for class imbalanced multi-instance datardquo Pattern Recognition vol 53 pp 36ndash45 2016

[20] C Wang M Shao Q He Y Qian and Y Qi ldquoFeature subsetselection based on fuzzy neighborhood rough setsrdquoKnowledge-Based Systems vol 111 pp 173ndash179 2016

[21] Y Yao and X Zhang ldquoClass-specific attribute reducts in roughset theoryrdquo Information Sciences An International Journal vol418419 pp 601ndash618 2017

[22] J Zhai X Wang and X Pang ldquoVoting-based instance selectionfrom large data sets with MapReduce and random weightnetworksrdquo Information Sciences vol 367-368 pp 1066ndash10772016

[23] H-Y Zhang and S-Y Yang ldquoFeature selection and approxi-mate reasoning of large-scale set-valued decision tables basedon 120572-dominance-based quantitative rough setsrdquo InformationSciences vol 378 pp 328ndash347 2017

[24] X Zhang CMei D Chen and J Li ldquoFeature selection inmixeddata amethod using a novel fuzzy rough set-based informationentropyrdquo Pattern Recognition pp 1ndash15 2016

[25] C Wang Y Qi M Shao et al ldquoA Fitting Model for FeatureSelection With Fuzzy Rough Setsrdquo IEEE Transactions on FuzzySystems vol 25 no 4 pp 741ndash753 2017

[26] A Sanchis M J Segovia J A Gil A Heras and J LVilar ldquoRough Sets and the role of the monetary policy infinancial stability (macroeconomic problem) and the predictionof insolvency in insurance sector (microeconomic problem)rdquoEuropean Journal of Operational Research vol 181 no 3 pp1554ndash1573 2007

[27] P Pattaraintakorn N Cercone and K Naruedomkul ldquoRulelearning ordinal prediction based on rough sets and soft-computingrdquo Applied Mathematics Letters An InternationalJournal of Rapid Publication vol 19 no 12 pp 1300ndash1307 2006

[28] A M Radzikowska and E E Kerre ldquoA comparative study offuzzy rough setsrdquo Fuzzy Sets and Systems vol 126 no 2 pp 137ndash155 2002

[29] C YWang ldquoTopological characterizations of generalized fuzzyrough setsrdquo Fuzzy Sets and Systems vol 312 pp 109ndash125 2017

[30] C Y Wang ldquoTopological structures of L-fuzzy rough sets andsimilarity sets of L-fuzzy relationsrdquo International Journal ofApproximate Reasoning vol 83 pp 160ndash175 2017

[31] W Pan K She and PWei ldquoMulti-granulation fuzzy preferencerelation rough set for ordinal decision systemrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 87ndash108 2017

[32] A Namburu S K Samay and S R Edara ldquoSoft fuzzy rough set-based MR brain image segmentationrdquo Applied Soft ComputingJournal vol 54 pp 456ndash466 2017

[33] Y Li S Wu Y Lin and J Liu ldquoDifferent classesrsquo ratio fuzzyrough set based robust feature selectionrdquo Knowledge-BasedSystems vol 120 pp 74ndash86 2017

[34] T Feng H-T Fan and J-S Mi ldquoUncertainty and reductionof variable precision multigranulation fuzzy rough sets basedon three-way decisionsrdquo International Journal of ApproximateReasoning vol 85 pp 36ndash58 2017

[35] B Sun W Ma and Y Qian ldquoMultigranulation fuzzy roughset over two universes and its application to decision makingrdquoKnowledge-Based Systems vol 123 pp 61ndash74 2017

[36] X R Zhao and B Q Hu ldquoFuzzy and interval-valued fuzzydecision-theoretic rough set approaches based on fuzzy proba-bility measurerdquo Information Sciences An International Journalvol 298 pp 534ndash554 2015

[37] H Zhang and L Shu ldquoGeneralized interval-valued fuzzy roughset and its application in decisionmakingrdquo International Journalof Fuzzy Systems vol 17 no 2 pp 279ndash291 2015

[38] C Y Wang and B Q Hu ldquoGranular variable precision fuzzyrough sets with general fuzzy relationsrdquo Fuzzy Sets and SystemsAn International Journal in Information Science andEngineeringvol 275 pp 39ndash57 2015

[39] T Feng and J-S Mi ldquoVariable precision multigranulationdecision-theoretic fuzzy rough setsrdquo Knowledge-Based Systemsvol 91 pp 93ndash101 2016

[40] C Y Wang and B Q Hu ldquoFuzzy rough sets based on general-ized residuated latticesrdquo Information Sciences An InternationalJournal vol 248 pp 31ndash49 2013

[41] S Teng F LiaoMHeM Lu andYNian ldquoIntegratedmeasuresfor rough sets based on general binary relationsrdquo SpringerPlusvol 5 no 1 article no 117 pp 1ndash17 2016

[42] F Macia-Perez J V Berna-Martinez A Fernandez Oliva andM A Abreu Ortega ldquoAlgorithm for the detection of outliersbased on the theory of rough setsrdquo Decision Support Systemsvol 75 Article ID 12609 pp 63ndash75 2015

[43] J J Buckley and E Eslami An Introduction to Fuzzy Logic andFuzzy Sets Springer Science and Business Media 2002

[44] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[45] B Bede and S G Gal ldquoAlmost periodic fuzzy-number-valuedfunctionsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 147 no 3 pp 385ndash4032004

[46] Z Pawlak ldquoRough set theory and its applications to dataanalysisrdquo Cybernetics and Systems vol 29 no 7 pp 661ndash6881998

[47] L Polkowski S Tsumoto and T Y Lin Rough Set Methodsand Applications New Developments in Knowledge Discoveryin Information Systems Physica-Verlag GmbH HeidelbergGermany 2000

[48] G Liu and Y Sai ldquoInvertible approximation operators of gen-eralized rough sets and fuzzy rough setsrdquo Information SciencesAn International Journal vol 180 no 11 pp 2221ndash2229 2010

[49] Z Zhang ldquoA rough set approach to intuitionistic fuzzy softset based decision makingrdquo Applied Mathematical ModellingSimulation andComputation for Engineering and EnvironmentalSystems vol 36 no 10 pp 4605ndash4633 2012

[50] Y Ouyang Z Wang and H-p Zhang ldquoOn fuzzy roughsets based on tolerance relationsrdquo Information Sciences AnInternational Journal vol 180 no 4 pp 532ndash542 2010

[51] J Dai and H Tian ldquoFuzzy rough set model for set-valued datardquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 229 pp 54ndash68 2013

[52] A Zeng T Li D Liu J Zhang and H Chen ldquoA fuzzyrough set approach for incremental feature selection on hybridinformation systemsrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 258 pp 39ndash60 2015

[53] M Shabir andT Shaheen ldquoAnewmethodology for fuzzificationof rough sets based on 120572-indiscernibilityrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 312 pp 1ndash16 2017

[54] X Wu and J-L Zhang ldquoRough set models based on randomfuzzy sets and belief function of fuzzy setsrdquo InternationalJournal of General Systems vol 41 no 2 pp 123ndash141 2012

26 Complexity

[55] S-M Chen S-H Cheng and Z-J Chen ldquoFuzzy interpolativereasoning based on the ratio of fuzziness of rough-fuzzy setsrdquoInformation Sciences An International Journal vol 299 pp394ndash411 2015

[56] E C C Tsang C Wang D Chen C Wu and Q Hu ldquoCom-munication between information systems using fuzzy roughsetsrdquo IEEE Transactions on Fuzzy Systems vol 21 no 3 pp 527ndash540 2013

[57] Y Han P Shi and S Chen ldquoBipolar-Valued Rough Fuzzy Setand Its Applications to the Decision Information Systemrdquo IEEETransactions on Fuzzy Systems vol 23 no 6 pp 2358ndash23702015

[58] MAggarwal ldquoProbabilistic variable precision fuzzy rough setsrdquoIEEE Transactions on Fuzzy Systems vol 24 no 1 pp 29ndash392016

[59] D C Liang D Liu W Pedrycz and P Hu ldquoTriangularfuzzy decision-theoretic rough setsrdquo International Journal ofApproximate Reasoning vol 54 no 8 pp 1087ndash1106 2013

[60] Q Hu D Yu andM Guo ldquoFuzzy preference based rough setsrdquoInformation Sciences An International Journal vol 180 no 10pp 2003ndash2022 2010

[61] D Liang and D Liu ldquoDeriving three-way decisions fromintuitionistic fuzzy decision-theoretic rough setsrdquo InformationSciences An International Journal vol 300 pp 28ndash48 2015

[62] B Sun W Ma and H Zhao ldquoA fuzzy rough set approach toemergency material demand prediction over two universesrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 10-11 pp7062ndash7070 2013

[63] H Zhang L Shu and S Liao ldquoHesitant fuzzy rough set overtwo universes and its application in decision makingrdquo SoftComputing vol 21 no 7 pp 1803ndash1816 2017

[64] J Zhan and K Zhu ldquoA novel soft rough fuzzy set Z-soft roughfuzzy ideals of hemirings and corresponding decision makingrdquoSoft Computing vol 21 no 8 pp 1923ndash1936 2017

[65] B Sun and W Ma ldquoSoft fuzzy rough sets and its application indecisionmakingrdquoArtificial Intelligence Review vol 41 no 1 pp67-68 2014

[66] H L Yang S G Li Z L Guo andCHMa ldquoTransformation ofbipolar fuzzy rough set modelsrdquo Knowledge-Based Systems vol27 pp 60ndash68 2012

[67] B Sun W Ma and X Chen ldquoFuzzy rough set on probabilisticapproximation space over two universes and its application toemergency decision-makingrdquo Expert Systems vol 32 no 4 pp507ndash521 2015

[68] T-F Fan C-J Liau and D-R Liu ldquoDominance-based fuzzyrough set analysis of uncertain and possibilistic data tablesrdquoInternational Journal of Approximate Reasoning vol 52 no 9pp 1283ndash1297 2011

[69] Y Cheng ldquoThe incremental method for fast computing therough fuzzy approximationsrdquoData and Knowledge Engineeringvol 70 no 1 pp 84ndash100 2011

[70] H-L Yang X Liao S Wang and J Wang ldquoFuzzy probabilisticrough set model on two universes and its applicationsrdquo Inter-national Journal of Approximate Reasoning vol 54 no 9 pp1410ndash1420 2013

[71] W-ZWu Y Leung andM-W Shao ldquoGeneralized fuzzy roughapproximation operators determined by fuzzy implicatorsrdquoInternational Journal of Approximate Reasoning vol 54 no 9pp 1388ndash1409 2013

[72] B Fan E C C Tsang W Xu and J Yu ldquoDouble-quantitativerough fuzzy set based decisions A logical operations methodrdquoInformation Sciences vol 378 pp 264ndash281 2017

[73] B Sun W Ma and D Chen ldquoRough approximation of afuzzy concept on a hybrid attribute information system andits uncertainty measurerdquo Information Sciences An InternationalJournal vol 284 pp 60ndash80 2014

[74] AA Estaji S Khodaii and S Bahrami ldquoOn rough set and fuzzysublatticerdquo Information Sciences An International Journal vol181 no 18 pp 3981ndash3994 2011

[75] F Li and Y Yin ldquoThe 120599-lower and T-upper fuzzy roughapproximation operators on a semigrouprdquo Information SciencesAn International Journal vol 195 pp 241ndash255 2012

[76] Q Zhang J Wang G Wang and H Yu ldquoThe approximationset of a vague set in rough approximation spacerdquo InformationSciences An International Journal vol 300 pp 1ndash19 2015

[77] Z Li and R Cui ldquoSimilarity of fuzzy relations based on fuzzytopologies induced by fuzzy rough approximation operatorsrdquoInformation Sciences vol 305 pp 219ndash233 2015

[78] W-ZWuY-HXuM-W Shao andGWang ldquoAxiomatic char-acterizations of (S T)-fuzzy rough approximation operatorsrdquoInformation Sciences vol 334-335 pp 17ndash43 2016

[79] J Hao and Q Li ldquoThe relationship between L-fuzzy roughset and L-topologyrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 178 pp 74ndash83 2011

[80] Y Cheng ldquoForward approximation and backward approxima-tion in fuzzy rough setsrdquoNeurocomputing vol 148 pp 340ndash3532015

[81] F Feng C Li B Davvaz andM I Ali ldquoSoft sets combined withfuzzy sets and rough sets a tentative approachrdquo Soft Computingvol 14 no 9 pp 899ndash911 2010

[82] B SunWMa andH Zhao ldquoDecision-theoretic rough fuzzy setmodel and applicationrdquo Information Sciences An InternationalJournal vol 283 pp 180ndash196 2014

[83] R Jensen A Tuson and Q Shen ldquoFinding rough and fuzzy-rough set reducts with SATrdquo Information Sciences An Interna-tional Journal vol 255 pp 100ndash120 2014

[84] Y Qian Q Wang H Cheng J Liang and C Dang ldquoFuzzy-rough feature selection acceleratorrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 258 pp 61ndash78 2015

[85] Q Hu S An and D Yu ldquoSoft fuzzy rough sets for robustfeature evaluation and selectionrdquo Information Sciences AnInternational Journal vol 180 no 22 pp 4384ndash4400 2010

[86] T-P Hong L-H Tseng and B-C Chien ldquoMining from incom-plete quantitative data by fuzzy rough setsrdquo Expert Systems withApplications vol 37 no 3 pp 2644ndash2653 2010

[87] A Onan ldquoA fuzzy-rough nearest neighbor classifier combinedwith consistency-based subset evaluation and instance selectionfor automated diagnosis of breast cancerrdquo Expert Systems withApplications vol 42 no 20 pp 6844ndash6852 2015

[88] J Derrac C Cornelis S Garcıa and F Herrera ldquoEnhancingevolutionary instance selection algorithms by means of fuzzyrough set based feature selectionrdquo Information Sciences vol 186no 1 pp 73ndash92 2012

[89] R Jensen and N Mac Parthalain ldquoTowards scalable fuzzy-rough feature selectionrdquo Information Sciences vol 323 ArticleID 11619 pp 1ndash15 2015

[90] S K Pal S K Meher and S Dutta ldquoClass-dependent rough-fuzzy granular space dispersion index and classificationrdquo Pat-tern Recognition vol 45 no 7 pp 2690ndash2707 2012

Complexity 27

[91] P Maji and P Garai ldquoOn fuzzy-rough attribute selection Cri-teria of Max-Dependency Max-Relevance Min-Redundancyand Max-Significancerdquo Applied Soft Computing Journal vol 13no 9 pp 3968ndash3980 2013

[92] A Ganivada S S Ray and S K Pal ldquoFuzzy rough sets anda granular neural network for unsupervised feature selectionrdquoNeural Networks vol 48 pp 91ndash108 2013

[93] P K Kumar P Vadakkepat and L A Poh ldquoFuzzy-roughdiscriminative feature selection and classification algorithmwith application tomicroarray and image datasetsrdquoApplied SoftComputing Journal vol 11 no 4 pp 3429ndash3440 2011

[94] QHu D YuW Pedrycz andD Chen ldquoKernelized fuzzy roughsets and their applicationsrdquo IEEE Transactions on Knowledgeand Data Engineering vol 23 no 11 pp 1649ndash1667 2011

[95] C Cornelis J Medina and N Verbiest ldquoMulti-adjoint fuzzyrough sets definition properties and attribute selectionrdquo Inter-national Journal of Approximate Reasoning vol 55 no 1 part 4pp 412ndash426 2014

[96] N Mac Parthalain and R Jensen ldquoUnsupervised fuzzy-roughset-based dimensionality reductionrdquo Information Sciences vol229 pp 106ndash121 2013

[97] J Dai and Q Xu ldquoAttribute selection based on informationgain ratio in fuzzy rough set theory with application to tumorclassificationrdquo Applied Soft Computing Journal vol 13 no 1 pp211ndash221 2013

[98] D Chen Q He and X Wang ldquoFRSVMs fuzzy rough setbased support vector machinesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 161 no 4 pp 596ndash607 2010

[99] Q Hu S An X Yu and D Yu ldquoRobust fuzzy rough classifiersrdquoFuzzy Sets and Systems An International Journal in InformationScience and Engineering vol 183 pp 26ndash43 2011

[100] W Wei J Cui J Liang and J Wang ldquoFuzzy rough approxima-tions for set-valued datardquo Information Sciences vol 360 pp 181ndash201 2016

[101] Y Yao J Mi and Z Li ldquoA novel variable precision (120579 120590)-fuzzy rough set model based on fuzzy granulesrdquo Fuzzy Sets andSystems vol 236 pp 58ndash72 2014

[102] D Chen L Zhang S Zhao Q Hu and P Zhu ldquoA novelalgorithm for finding reducts with fuzzy rough setsrdquo IEEETransactions on Fuzzy Systems vol 20 no 2 pp 385ndash389 2012

[103] S Zhao H Chen C Li M Zhai and X Du ldquoRFRR Robustfuzzy rough reductionrdquo IEEE Transactions on Fuzzy Systemsvol 21 no 5 pp 825ndash841 2013

[104] D Chen and Y Yang ldquoAttribute reduction for heterogeneousdata based on the combination of classical and fuzzy rough setmodelsrdquo IEEE Transactions on Fuzzy Systems vol 22 no 5 pp1325ndash1334 2014

[105] Z Gong and X Zhang ldquoVariable precision intuitionistic fuzzyrough sets model and its applicationrdquo International Journal ofMachine Learning and Cybernetics vol 5 no 2 pp 263ndash2802014

[106] B Huang Y-l Zhuang H-x Li and D-k Wei ldquoA dominanceintuitionistic fuzzy-rough set approach and its applicationsrdquoApplied Mathematical Modelling Simulation and Computationfor Engineering and Environmental Systems vol 37 no 12-13 pp7128ndash7141 2013

[107] Y Yang and C Hinde ldquoA new extension of fuzzy sets usingrough sets R-fuzzy setsrdquo Information Sciences An InternationalJournal vol 180 no 3 pp 354ndash365 2010

[108] Y Cheng D Miao and Q Feng ldquoPositive approximation andconverse approximation in interval-valued fuzzy rough setsrdquoInformation Sciences An International Journal vol 181 no 11pp 2086ndash2110 2011

[109] Z Zhang ldquoGeneralized intuitionistic fuzzy rough sets basedon intuitionistic fuzzy coveringsrdquo Information Sciences AnInternational Journal vol 198 pp 186ndash206 2012

[110] Z Xue Y Shang and A Feng ldquoSemi-supervised outlier detec-tion based on fuzzy rough C-means clusteringrdquo Mathematicsand Computers in Simulation vol 80 no 9 pp 1911ndash1921 2010

[111] X Zhang B Zhou and P Li ldquoA general frame for intuitionisticfuzzy rough setsrdquo Information Sciences An International Jour-nal vol 216 pp 34ndash49 2012

[112] WWei J Liang Y Qian and C Dang ldquoCan fuzzy entropies beeffective measures for evaluating the roughness of a rough setrdquoInformation Sciences vol 232 pp 143ndash166 2013

[113] B Huang C-x Guo Y-l Zhuang H-x Li and X-z ZhouldquoIntuitionistic fuzzy multigranulation rough setsrdquo InformationSciences An International Journal vol 277 pp 299ndash320 2014

[114] C Y Wang ldquoType-2 fuzzy rough sets based on extended t-normsrdquo Information Sciences An International Journal vol 305pp 165ndash183 2015

[115] B Yang and B Q Hu ldquoA fuzzy covering-based rough set modeland its generalization over fuzzy latticerdquo Information Sciencesvol 367-368 pp 463ndash486 2016

[116] J Lu D Y Li Y H Zhai H Li andH X Bai ldquoAmodel for type-2 fuzzy rough setsrdquo Information Sciences vol 328 pp 359ndash3772016

[117] D Chen S Kwong Q He and H Wang ldquoGeometrical inter-pretation and applications of membership functions with fuzzyrough setsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 193 pp 122ndash135 2012

[118] L Drsquoeer N Verbiest C Cornelis and L s Godo ldquoA com-prehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets definitions properties and robustnessanalysisrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 275 pp 1ndash38 2015

[119] L Ma ldquoTwo fuzzy covering rough set models and theirgeneralizations over fuzzy latticesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 294 pp 1ndash17 2016

[120] Q He C Wu D Chen and S Zhao ldquoFuzzy rough setbased attribute reduction for information systems with fuzzydecisionsrdquoKnowledge-Based Systems vol 24 no 5 pp 689ndash6962011

[121] H-L Yang S-G Li S Wang and J Wang ldquoBipolar fuzzyrough set model on two different universes and its applicationrdquoKnowledge-Based Systems vol 35 pp 94ndash101 2012

[122] Z Zhang ldquoOn interval type-2 rough fuzzy setsrdquo Knowledge-Based Systems vol 35 pp 1ndash13 2012

[123] H Bai Y Ge J Wang D Li Y Liao and X Zheng ldquoA methodfor extracting rules from spatial data based on rough fuzzy setsrdquoKnowledge-Based Systems vol 57 pp 28ndash40 2014

[124] X R Zhao and B Q Hu ldquoFuzzy probabilistic rough sets andtheir corresponding three-way decisionsrdquo Knowledge-BasedSystems vol 91 pp 126ndash142 2016

[125] B Huang C-X Guo H-X Li G-F Feng and X-Z ZhouldquoAn intuitionistic fuzzy graded covering rough setrdquo Knowledge-Based Systems vol 107 pp 155ndash178 2016

[126] A S Khuman Y Yang and R John ldquoQuantification of R-fuzzysetsrdquoExpert SystemswithApplications vol 55 pp 374ndash387 2016

28 Complexity

[127] Y Liu and Y Lin ldquoIntuitionistic fuzzy rough set model basedon conflict distance and applicationsrdquo Applied Soft ComputingJournal vol 31 pp 266ndash273 2015

[128] B Sun W Ma and Q Liu ldquoAn approach to decision makingbased on intuitionistic fuzzy rough sets over two universesrdquoJournal of the Operational Research Society vol 64 no 7 pp1079ndash1089 2013

[129] H Zhang L Shu S Liao and C Xiawu ldquoDual hesitant fuzzyrough set and its applicationrdquo Soft Computing vol 21 no 12pp 3287ndash3305 2015

[130] B Q Hu ldquoGeneralized interval-valued fuzzy variable precisionrough sets determined by fuzzy logical operatorsrdquo InternationalJournal of General Systems vol 44 no 7-8 pp 849ndash875 2015

[131] T Zhao and J Xiao ldquoGeneral type-2 fuzzy rough sets based on120572-plane representation theoryrdquo Soft Computing vol 18 no 2pp 227ndash237 2014

[132] X B Yang X N Song Y S Qi and J Y Yang ldquoConstructiveand axiomatic approaches to hesitant fuzzy rough setrdquo SoftComputing vol 18 no 6 pp 1067ndash1077 2014

[133] H D Zhang L Shu and S L Liao ldquoOn interval-valued hesitantfuzzy rough approximation operatorsrdquo Soft Computing 2014

[134] C Y Wang and B Q Hu ldquoOn fuzzy-valued operations andfuzzy-valued fuzzy setsrdquo Fuzzy Sets and Systems An Interna-tional Journal in Information Science and Engineering vol 268pp 72ndash92 2015

[135] S Mitra W Pedrycz and B Barman ldquoShadowed c-meansintegrating fuzzy and rough clusteringrdquo Pattern Recognitionvol 43 no 4 pp 1282ndash1291 2010

[136] C Chen NM Parthalain Y Li C Price C Quek andQ ShenldquoRough-fuzzy rule interpolationrdquo Information Sciences vol 351pp 1ndash17 2016

[137] C Zhang D Li Y Mu and D Song ldquoAn interval-valuedhesitant fuzzy multigranulation rough set over two universesmodel for steam turbine fault diagnosisrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 42 pp 693ndash704 2017

[138] F Bobillo andU Straccia ldquoGeneralized fuzzy rough descriptionlogicsrdquo Information Sciences An International Journal vol 189pp 43ndash62 2012

[139] G Liu ldquoUsing one axiom to characterize rough set and fuzzyrough set approximationsrdquo Information Sciences An Interna-tional Journal vol 223 pp 285ndash296 2013

[140] S An H Shi Q Hu X Li and J Dang ldquoFuzzy rough regres-sion with application to wind speed predictionrdquo InformationSciences An International Journal vol 282 pp 388ndash400 2014

[141] L S Riza A Janusz C Bergmeir et al ldquoImplementing algo-rithms of rough set theory and fuzzy rough set theory in the Rpackage ldquoroughSetsrdquordquo Information Sciences vol 287 pp 68ndash892014

[142] R K Shiraz V Charles and L Jalalzadeh ldquoFuzzy rough DEAmodel A possibility and expected value approachesrdquo ExpertSystems with Applications vol 41 no 2 pp 434ndash444 2014

[143] A Zeng T Li J Hu H Chen and C Luo ldquoDynamicalupdating fuzzy rough approximations for hybrid data underthe variation of attribute valuesrdquo Information Sciences AnInternational Journal vol 378 pp 363ndash388 2017

[144] J Zhou W Pedrycz and D Miao ldquoShadowed sets in the char-acterization of rough-fuzzy clusteringrdquo Pattern Recognition vol44 no 8 pp 1738ndash1749 2011

[145] N Verbiest C Cornelis and F Herrera ldquoFRPS A Fuzzy RoughPrototype Selection methodrdquo Pattern Recognition vol 46 no10 pp 2770ndash2782 2013

[146] S Pramanik D K Jana and M Maiti ldquoBi-criteria solid trans-portation problem with substitutable and damageable itemsin disaster response operations on fuzzy rough environmentrdquoSocio-Economic Planning Sciences vol 55 pp 1ndash13 2016

[147] G Liu ldquoRough set theory based on two universal sets and itsapplicationsrdquo Knowledge-Based Systems vol 23 no 2 pp 110ndash115 2010

[148] S KMeher ldquoExplicit rough-fuzzy pattern classificationmodelrdquoPattern Recognition Letters vol 36 no 1 pp 54ndash61 2014

[149] S Kundu and S K Pal ldquoFuzzy-rough community in socialnetworksrdquo Pattern Recognition Letters vol 67 pp 145ndash152 2015

[150] A Ganivada S S Ray and S Pal ldquoFuzzy rough granular self-organizingmap and fuzzy rough entropyrdquoTheoretical ComputerScience vol 466 pp 37ndash63 2012

[151] M Amiri and R Jensen ldquoMissing data imputation using fuzzy-rough methodsrdquo Neurocomputing vol 205 pp 152ndash164 2016

[152] E Ramentol I Gondres S Lajes et al ldquoFuzzy-rough imbal-anced learning for the diagnosis ofHighVoltageCircuit Breakermaintenance The SMOTE-FRST-2T algorithmrdquo EngineeringApplications of Artificial Intelligence vol 48 pp 134ndash139 2016

[153] C Affonso R J Sassi and R M Barreiros ldquoBiological imageclassification using rough-fuzzy artificial neural networkrdquoExpert Systems with Applications vol 42 no 24 pp 9482ndash94882015

[154] N Shukla and S Kiridena ldquoA fuzzy rough sets-based multi-agent analytics framework for dynamic supply chain configura-tionrdquo International Journal of Production Research vol 54 pp6984ndash6996 2016

[155] P Pahlavani H Amini Amirkolaee and S Talebi Nahr ldquoAnew feature selection from lidar data and digital aerial imagesacquired for an urbanc environment using an ANFIS-basedclassification and a fuzzy rough set methodrdquo InternationalJournal of Remote Sensing vol 36 no 14 pp 3587ndash3615 2015

[156] H Xie and B Q Hu ldquoNew extended patterns of fuzzy roughset models on two universesrdquo International Journal of GeneralSystems vol 43 no 6 pp 570ndash585 2014

[157] S Zhao E C C Tsang D Chen and XWang ldquoBuilding a rule-based classifiera fuzzy-rough set approachrdquo IEEE Transactionson Knowledge and Data Engineering vol 22 no 5 pp 624ndash6382010

[158] P Maji and S K Pal ldquoFuzzy-rough sets for informationmeasures and selection of relevant genes frommicroarray datardquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 40 no 3 pp 741ndash752 2010

[159] H-H Huang and Y-H Kuo ldquoCross-lingual document repre-sentation and semantic similarity measure A fuzzy set andrough set based approachrdquo IEEE Transactions on Fuzzy Systemsvol 18 no 6 pp 1098ndash1111 2010

[160] R Wang D Chen and S Kwong ldquoFuzzy-Rough-Set-BasedActive Learningrdquo IEEE Transactions on Fuzzy Systems vol 22no 6 pp 1699ndash1704 2014

[161] E Ramentol S Vluymans N Verbiest et al ldquoIFROWANNImbalanced Fuzzy-Rough Ordered Weighted Average NearestNeighbor Classificationrdquo IEEE Transactions on Fuzzy Systemsvol 23 no 5 pp 1622ndash1637 2015

[162] X F Zhang G Yu Z Y Hu C H Pei and G Q MaldquoParallel disassembly sequence planning for complex productsbased on fuzzy-rough setsrdquo International Journal of AdvancedManufacturing Technology vol 72 no 1-4 pp 231ndash239 2014

[163] J Derrac NVerbiest S Garcıa C Cornelis and FHerrera ldquoOnthe use of evolutionary feature selection for improving fuzzy

Complexity 29

rough set based prototype selectionrdquo Soft Computing vol 17 no2 pp 223ndash238 2013

[164] N Verbiest E Ramentol C Cornelis and F Herrera ldquoPrepro-cessing noisy imbalanced datasets using SMOTE enhancedwithfuzzy rough prototype selectionrdquo Applied Soft Computing vol22 pp 511ndash517 2014

[165] J-H Zhai ldquoFuzzy decision tree based on fuzzy-rough tech-niquerdquo Soft Computing vol 15 no 6 pp 1087ndash1096 2011

[166] J Zhao Z Zhang C Han and Z Zhou ldquoComplement informa-tion entropy for uncertainty measure in fuzzy rough set and itsapplicationsrdquo Soft Computing vol 19 no 7 pp 1997ndash2010 2015

[167] Q Hu L Zhang S An D Zhang and D Yu ldquoOn robust fuzzyrough set modelsrdquo IEEE Transactions on Fuzzy Systems vol 20no 4 pp 636ndash651 2012

[168] C Changdar R K Pal and G S Mahapatra ldquoA geneticant colony optimization based algorithm for solid multipletravelling salesmen problem in fuzzy rough environmentrdquo SoftComputing pp 1ndash15 2016

[169] B Sun and W Ma ldquoAn approach to evaluation of emergencyplans for unconventional emergency events based on soft fuzzyrough setrdquo Kybernetes The International Journal of CyberneticsSystems and Management Sciences vol 45 no 3 pp 461ndash4732016

[170] W S Du and B Q Hu ldquoDominance-based rough fuzzy setapproach and its application to rule inductionrdquo EuropeanJournal of Operational Research vol 261 no 2 pp 690ndash7032017

[171] J Hu T Li C Luo H Fujita and S Li ldquoIncremental fuzzy prob-abilistic rough sets over two universesrdquo International Journal ofApproximate Reasoning vol 81 pp 28ndash48 2017

[172] D Liang Z Xu and D Liu ldquoThree-way decisions with intu-itionistic fuzzy decision-theoretic rough sets based on pointoperatorsrdquo Information Sciences vol 375 pp 183ndash201 2017

[173] D Liang Z Xu and D Liu ldquoThree-way decisions based ondecision-theoretic rough sets with dual hesitant fuzzy informa-tionrdquo Information Sciences vol 396 pp 127ndash143 2017

[174] J Qiao andBQHu ldquoGranular variable precisionL-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2016

[175] J Qiao and B Q Hu ldquoOn (⊙amp)-fuzzy rough sets based onresiduated and coresiduated latticesrdquo Fuzzy Sets and Systems2017

[176] J Shi Y Lei Y Zhou and M Gong ldquoEnhanced roughndashfuzzy c-means algorithm with strict rough sets propertiesrdquo Applied SoftComputing Journal vol 46 pp 827ndash850 2016

[177] C Y Wang ldquoNotes on a comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets defi-nitions properties and robustness analysisrdquo Fuzzy Sets andSystems An International Journal in Information Science andEngineering vol 294 pp 36ndash43 2016

[178] B Yang and B Q Hu ldquoOn some types of fuzzy covering-basedrough setsrdquo Fuzzy Sets and Systems vol 312 pp 36ndash65 2017

[179] N N Morsi and M M Yakout ldquoAxiomatics for fuzzy roughsetsrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 100 no 1-3 pp 327ndash342 1998

[180] X Wang and J Hong ldquoLearning optimization in simplifyingfuzzy rulesrdquo Fuzzy Sets and Systems An International Journalin Information Science and Engineering vol 106 no 3 pp 349ndash356 1999

[181] D Molodtsov ldquoSoft set theorymdashfirst resultsrdquo Computers ampMathematics with Applications vol 37 no 4-5 pp 19ndash31 1999

[182] P K Maji R Biswas and A R Roy ldquoFuzzy soft setsrdquo Journal ofFuzzy Mathematics vol 9 no 3 pp 589ndash602 2001

[183] M De Cock C Cornelis and E Kerre ldquoFuzzy rough setsBeyond the obviousrdquo in Proceedings of the 2004 IEEE Interna-tional Conference on Fuzzy Systems - Proceedings pp 103ndash108hun July 2004

[184] R Jensen and Q Shen ldquoFuzzy-rough attribute reduction withapplication to web categorizationrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 141 no 3 pp 469ndash485 2004

[185] A Mieszkowicz-Rolka and L Rolka ldquoVariable precision fuzzyrough setsrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 3100 pp 144ndash160 2004

[186] J-S Mi and W-X Zhang ldquoAn axiomatic characterization ofa fuzzy generalization of rough setsrdquo Information Sciences AnInternational Journal vol 160 no 1-4 pp 235ndash249 2004

[187] Q Shen and R Jensen ldquoSelecting informative features withfuzzy-rough sets and its application for complex systems mon-itoringrdquo Pattern Recognition vol 37 no 7 pp 1351ndash1363 2004

[188] W-ZWu Y Leung and J-SMi ldquoOn characterizations of (IT)-fuzzy rough approximation operatorsrdquo Fuzzy Sets and Systemsvol 154 no 1 pp 76ndash102 2005

[189] R B Bhatt and M Gopal ldquoOn the compact computationaldomain of fuzzy-rough setsrdquoPattern Recognition Letters vol 26no 11 pp 1632ndash1640 2005

[190] D S Yeung D Chen E C C Tsang JW T Lee andW XizhaoldquoOn the generalization of fuzzy rough setsrdquo IEEE Transactionson Fuzzy Systems vol 13 no 3 pp 343ndash361 2005

[191] T Deng Y ChenW Xu andQ Dai ldquoA novel approach to fuzzyrough sets based on a fuzzy coveringrdquo Information Sciences AnInternational Journal vol 177 no 11 pp 2308ndash2326 2007

[192] T Li and J Ma ldquoFuzzy Approximation Operators Based onCoveringsrdquo inRough Sets Fuzzy Sets DataMining andGranularComputing vol 4482 of Lecture Notes in Computer Science pp55ndash62 Springer Berlin Heidelberg Berlin Heidelberg 2007

[193] H Aktas and N Cagman ldquoSoft sets and soft groupsrdquo Informa-tion Sciences vol 177 no 13 pp 2726ndash2735 2007

[194] S Greco R Slowinski and Y Yao ldquoBayesian decision theoryfor dominance-based rough set approachrdquo in Proceeding ofthe International Conference on Rough Sets and KnowledgeTechnology pp 134ndash141 Springer 2007

[195] C Cornelis R Jensen G Hurtado and D Slezak ldquoAttributeselection with fuzzy decision reductsrdquo Information Sciences vol180 no 2 pp 209ndash224 2010

[196] X Wang E C Tsang S Zhao D Chen and D S YeungldquoLearning fuzzy rules from fuzzy samples based on rough settechniquerdquo Information Sciences vol 177 no 20 pp 4493ndash45142007

[197] Q Hu Z Xie andD Yu ldquoHybrid attribute reduction based on anovel fuzzy-roughmodel and information granulationrdquo PatternRecognition vol 40 no 12 pp 3509ndash3521 2007

[198] P Lingras M Chen and D Miao ldquoRough multi-categorydecision theoretic framework inrdquo in International Conference onRough Sets and Knowledge Technology pp 676ndash683 Springer2008

[199] P Lingras M Chen and D Miao ldquoRough cluster quality indexbased on decision theoryrdquo IEEE Transactions on Knowledge andData Engineering vol 21 no 7 pp 1014ndash1026 2009

[200] Y-H She and G-J Wang ldquoAn axiomatic approach of fuzzyrough sets based on residuated latticesrdquo Computers and Mathe-matics with Applications vol 58 no 1 pp 189ndash201 2009

30 Complexity

[201] S Zhao E C C Tsang and D Chen ldquoThe model of fuzzyvariable precision rough setsrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 451ndash467 2009

[202] H YWu Y YWu and J P Luo ldquoAn interval type-2 fuzzy roughset model for attribute reductionrdquo IEEE Transactions on FuzzySystems vol 17 no 2 pp 301ndash315 2009

[203] R Yan J Zheng J Liu and Y Zhai ldquoResearch on the model ofrough set over dual-universesrdquo Knowledge-Based Systems vol23 no 8 pp 817ndash822 2010

[204] X Yang and J Yao ldquoA multi-agent decision-theoretic rough setmodelrdquo Lecture Notes in Computer Science (including subseriesLecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) vol 6401 pp 711ndash718 2010

[205] W Xu S Liu Q Wang andW Zhang ldquoThe first type of gradedrough set based on roughmembership functionrdquo in Proceedingsof the 2010 7th International Conference on Fuzzy Systems andKnowledge Discovery FSKD 2010 pp 1922ndash1926 chn August2010

[206] M Xia and Z Xu ldquoGeneralized point operators for aggregatingintuitionistic fuzzy informationrdquo International Journal of Intel-ligent Systems vol 25 pp 1061ndash1080 2010

[207] W-Z Wu ldquoOn some mathematical structures of T-fuzzy roughset algebras in infinite universes of discourserdquo FundamentaInformaticae vol 108 no 3-4 pp 337ndash369 2011

[208] F Feng X Liu V Leoreanu-Fotea and Y B Jun ldquoSoft sets andsoft rough setsrdquo Information Sciences vol 181 no 6 pp 1125ndash1137 2011

[209] D Meng X Zhang and K Qin ldquoSoft rough fuzzy sets and softfuzzy rough setsrdquo Computers amp Mathematics with Applicationsvol 62 no 12 pp 4635ndash4645 2011

[210] H Li and X Zhou ldquoRisk decision making based on decision-theoretic rough set A three-way view decision modelrdquo Interna-tional Journal of Computational Intelligence Systems vol 4 no1 pp 1ndash11 2011

[211] H Li X Zhou J Zhao and D Liu ldquoAttribute reduction indecision-theoretic rough set model A further investigationrdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6954 pp 466ndash475 2011

[212] X Jia W Li L Shang and J Chen ldquoAn optimization view-point of decision-theoretic rough set modelrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 6954 pp457ndash465 2011

[213] D Liu T Li and D Ruan ldquoProbabilistic model criteriawith decision-theoretic rough setsrdquo Information Sciences AnInternational Journal vol 181 no 17 pp 3709ndash3722 2011

[214] D Liu Y Yao and T Li ldquoThree-way investment decisionswith decision-theoretic rough setsrdquo International Journal ofComputational Intelligence Systems vol 4 no 1 pp 66ndash74 2011

[215] C Degang Y Yongping and W Hui ldquoGranular computingbased on fuzzy similarity relationsrdquo Soft Computing vol 15 no6 pp 1161ndash1172 2011

[216] WMa andB Sun ldquoOn relationship between probabilistic roughset and Bayesian risk decision over two universesrdquo InternationalJournal of General Systems vol 41 no 3 pp 225ndash245 2012

[217] W Ma and B Sun ldquoProbabilistic rough set over two universesand rough entropyrdquo International Journal of Approximate Rea-soning vol 53 no 4 pp 608ndash619 2012

[218] C Liu D Miao and N Zhang ldquoGraded rough set model basedon two universes and its propertiesrdquo Knowledge-Based Systemsvol 33 pp 65ndash72 2012

[219] WWei J Liang andYQian ldquoA comparative study of rough setsfor hybrid datardquo Information Sciences An International Journalvol 190 pp 1ndash16 2012

[220] Z M Ma and B Q Hu ldquoTopological and lattice structuresof L-fuzzy rough sets determined by lower and upper setsrdquoInformation Sciences An International Journal vol 218 pp 194ndash204 2013

[221] X Zhang and D Miao ldquoTwo basic double-quantitative roughset models of precision and grade and their investigation usinggranular computingrdquo International Journal of ApproximateReasoning vol 54 no 8 pp 1130ndash1148 2013

[222] X Zhang and D Miao ldquoQuantitative information architecturegranular computing and rough set models in the double-quantitative approximation space of precision and graderdquo Infor-mation Sciences An International Journal vol 268 pp 147ndash1682014

[223] D Liu T Li and D Liang ldquoIncorporating logistic regression todecision-theoretic rough sets for classificationsrdquo InternationalJournal of Approximate Reasoning vol 55 no 1 part 2 pp 197ndash210 2014

[224] X Ma G Wang H Yu and T Li ldquoDecision region distributionpreservation reduction in decision-theoretic rough set modelrdquoInformation Sciences An International Journal vol 278 pp 614ndash640 2014

[225] Y Qian H Zhang Y Sang and J Liang ldquoMultigranulationdecision-theoretic rough setsrdquo International Journal of Approx-imate Reasoning vol 55 no 1 part 2 pp 225ndash237 2014

[226] X Zhang and D Miao ldquoReduction target structure-based hier-archical attribute reduction for two-category decision-theoreticrough setsrdquo Information Sciences An International Journal vol277 pp 755ndash776 2014

[227] X Zhang and D Miao ldquoRegion-based quantitative and hierar-chical attribute reduction in the two-category decision theoreticrough setmodelrdquoKnowledge-Based Systems vol 71 pp 146ndash1612014

[228] X Zhang and D Miao ldquoAn expanded double-quantitativemodel regarding probabilities and grades and its hierarchicaldouble-quantitative attribute reductionrdquo Information SciencesAn International Journal vol 299 pp 312ndash336 2015

[229] Z Li and R Cui ldquoT-similarity of fuzzy relations and relatedalgebraic structuresrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 275 pp130ndash143 2015

[230] W XuW Li and S Luo ldquoKnowledge reductions in generalizedapproximation space over two universes based on evidencetheoryrdquo Journal of Intelligent and Fuzzy Systems vol 28 no 6pp 2471ndash2480 2015

[231] W Li andWXu ldquoMultigranulation decision-theoretic rough setin ordered information systemrdquo Fundamenta Informaticae vol139 no 1 pp 67ndash89 2015

[232] D Liang W Pedrycz D Liu and P Hu ldquoThree-way deci-sions based on decision-theoretic rough sets under linguisticassessment with the aid of group decision makingrdquoApplied SoftComputing Journal vol 29 pp 256ndash269 2015

[233] H Ju X Yang P YangH Li andX Zhou ldquoAmoderate attributereduction approach in decision-theoretic rough setrdquo in Roughsets fuzzy sets data mining and granular computing vol 9437of Lecture Notes in Comput Sci pp 376ndash388 Springer Cham2015

[234] W Li andWXu ldquoDouble-quantitative decision-theoretic roughsetrdquo Information Sciences vol 316 pp 54ndash67 2015

Complexity 31

[235] H-R Zhang and F Min ldquoThree-way recommender systemsbased on random forestsrdquoKnowledge-Based Systems vol 91 pp275ndash286 2016

[236] Y Zhang and J Yao ldquoGini objective functions for three-wayclassificationsrdquo International Journal of Approximate Reasoningvol 81 pp 103ndash114 2017

[237] B SunW Ma and X Xiao ldquoThree-way group decision makingbased on multigranulation fuzzy decision-theoretic rough setover two universesrdquo International Journal of Approximate Rea-soning vol 81 pp 87ndash102 2017

[238] J Qiao andBQHu ldquoGranular variable precision L-fuzzy roughsets based on residuated latticesrdquo Fuzzy Sets and Systems 2015

[239] D Moher A Liberati and J Tetzlaff ldquoPreferred reportingitems for systematic reviews and meta-analyses the PRISMAstatementrdquo Annals of Internal Medicine vol 151 pp 264ndash2692009

[240] D Budgen and P Brereton ldquoPerforming systematic literaturereviews in software engineeringrdquo in Proceedings of the 28thinternational conference on Software engineering pp 1051-1052May 2006

[241] P J Phillips and E M Newton ldquoMeta-analysis of face recog-nition algorithmsrdquo in Proceedings of the 5th IEEE InternationalConference on Automatic Face Gesture Recognition FGR 2002pp 235ndash241 usa May 2002

[242] A Liberati D G Altman J Tetzlaff et al ldquoThe PRISMAstatement for reporting systematic reviews and meta-analysesof studies that evaluate health care interventions explanationand elaborationrdquo Annals of Internal Medicine vol 151 no 4 pp65ndash94 2009

[243] A Hughes-Morley B Young W Waheed N Small and PBower ldquoFactors affecting recruitment into depression trialsSystematic review meta-synthesis and conceptual frameworkrdquoJournal of Affective Disorders vol 172 pp 274ndash290 2015

[244] N S Consedine N L Tuck C R Ragin and B A SpencerldquoBeyond the black box a systematic review of breast prostatecolorectal and cervical screening among native and immigrantafrican-descent caribbean populationsrdquo Journal of Immigrantand Minority Health vol 17 no 3 pp 905ndash924 2015

[245] F Xu L Wei Z Bi and L Zhu ldquoResearch on fuzzy roughparallel reduction based on mutual informationrdquo Journal ofComputational Information Systems vol 10 no 12 pp 5391ndash5401 2014

[246] Y Yang Z Chen Z Liang and G Wang ldquoAttribute reductionfor massive data based on rough set theory and mapreducerdquoLecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinformat-ics) vol 6401 pp 672ndash678 2010

[247] J Zhang T Li D Ruan Z Gao andC Zhao ldquoA parallel methodfor computing rough set approximationsrdquo Information Sciencesvol 194 pp 209ndash223 2012

[248] J Zhang J-SWong T Li and Y Pan ldquoA comparison of parallellarge-scale knowledge acquisition using rough set theory ondifferent MapReduce runtime systemsrdquo International Journal ofApproximate Reasoning vol 55 no 3 pp 896ndash907 2014

[249] Y Yang and Z Chen ldquoParallelized computing of attribute corebased on rough set theory and MapReducerdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) vol 7414 pp155ndash160 2012

[250] D Dubois and H Prade ldquoTwofold fuzzy sets and roughsetsmdashsome issues in knowledge representationrdquo Fuzzy Sets and

Systems An International Journal in Information Science andEngineering vol 23 no 1 pp 3ndash18 1987

[251] ldquoRough sets fuzzy sets data mining and granular computingrdquoin Lecture Notes in Computer Science (including subseries LectureNotes in Artificial Intelligence and Lecture Notes in Bioinfor-matics) 13th International Conference (RSFDGrC rsquo11) MoscowRussia June 25-27 2011 S O Kuznetsov D Slęzak D HHepting and B G Mirkin Eds vol 6743 pp 1ndash370 2011

[252] B Tripathy D Acharjya and V Cynthya ldquoA framework forintelligent medical diagnosis using rough set with formalconcept analysisrdquo International Journal of Artificial Intelligenceamp Applications vol 2 pp 45ndash66 2011

[253] S Greco B Matarazzo and R Slowinski ldquoFuzzy dominance-based rough set approachrdquo in Advances in Fuzzy Systems andIntelligent Technologies F Masulli R Parenti and G Pasi Edspp 56ndash66 Shaker Publishing Maastricht 2000

[254] S Greco M Inuiguchi and R Slowinski ldquoPossibility andnecessitymeasures in dominance-based rough set approachrdquo inProceedings of the International Conference on Rough Sets andCurrent Trends in Computing pp 85ndash92 2002

[255] S Greco B Matarazzo and R Slowinski ldquoThe use of rough setsand fuzzy sets in MCDMrdquo inMulticriteria DecisionMaking pp397ndash455 Springer 1999

[256] S Greco B Matarazzo and R Slowinski ldquoRough approxima-tion of a preference relation by dominance relationsrdquo EuropeanJournal of Operational Research vol 117 no 1 pp 63ndash83 1999

[257] S Chakhar A Ishizaka A Labib and I Saad ldquoDominance-based rough set approach for group decisionsrdquo EuropeanJournal of Operational Research vol 251 no 1 pp 206ndash2242016

[258] W S Du and B Q Hu ldquoDominance-based rough set approachto incomplete ordered information systemsrdquo Information Sci-ences An International Journal vol 346347 pp 106ndash129 2016

[259] B Sun and W Ma ldquoRough approximation of a preferencerelation by multi-decision dominance for a multi-agent conflictanalysis problemrdquo Information Sciences An International Jour-nal vol 315 pp 39ndash53 2015

[260] M Szeląg S Greco and R Słowinski ldquoVariable consistencydominance-based rough set approach to preference learning inmulticriteria rankingrdquo Information Sciences vol 277 pp 525ndash552 2014

[261] X Zhang D Chen and E C Tsang ldquoGeneralized dominancerough set models for the dominance intuitionistic fuzzy infor-mation systemsrdquo Information Sciences An International Journalvol 378 pp 1ndash25 2017

[262] S Li T Li and D Liu ldquoIncremental updating approximationsin dominance-based rough sets approach under the variation ofthe attribute setrdquo Knowledge-Based Systems vol 40 pp 17ndash262013

[263] J Błaszczynski S Greco and R Słowinski ldquoMulti-criteriaclassification - A new scheme for application of dominance-based decision rulesrdquo European Journal of Operational Researchvol 181 no 3 pp 1030ndash1044 2007

[264] S Chakhar and I Saad ldquoDominance-based rough set approachfor groups in multicriteria classification problemsrdquo DecisionSupport Systems vol 54 no 1 pp 372ndash380 2012

[265] M Inuiguchi Y Yoshioka andY Kusunoki ldquoVariable-precisiondominance-based rough set approach and attribute reductionrdquoInternational Journal of Approximate Reasoning vol 50 no 8pp 1199ndash1214 2009

32 Complexity

[266] K Dembczynski S Greco and R Słowinski ldquoRough setapproach to multiple criteria classification with impreciseevaluations and assignmentsrdquo European Journal of OperationalResearch vol 198 no 2 pp 626ndash636 2009

[267] X Yang J Yang C Wu and D Yu ldquoDominance-based roughset approach and knowledge reductions in incomplete orderedinformation systemrdquo Information Sciences An InternationalJournal vol 178 no 4 pp 1219ndash1234 2008

[268] S Li and T Li ldquoIncremental update of approximations indominance-based rough sets approach under the variation ofattribute valuesrdquo Information Sciences An International Journalvol 294 pp 348ndash361 2015

[269] R Jensen and Q Shen ldquoFuzzy-rough data reduction with antcolony optimizationrdquo Fuzzy Sets and Systems An InternationalJournal in Information Science and Engineering vol 149 no 1pp 5ndash20 2005

[270] CWang and FOu ldquoAn algorithm for decision tree constructionbased on rough set theoryrdquo in Proceedings of the InternationalConference on Computer Science and Information Technology(ICCSIT rsquo08) pp 295ndash298 September 2008

[271] H-L Chen B Yang J Liu and D-Y Liu ldquoA support vectormachine classifier with rough set-based feature selection forbreast cancer diagnosisrdquo Expert Systems with Applications vol38 no 7 pp 9014ndash9022 2011

[272] C Shang and D Barnes ldquoFuzzy-rough feature selection aidedsupport vector machines for Mars image classificationrdquo Com-puter Vision and Image Understanding vol 117 no 3 pp 202ndash213 2013

[273] QHe andCWu ldquoMembership evaluation and feature selectionfor fuzzy support vector machine based on fuzzy rough setsrdquoSoft Computing vol 15 no 6 pp 1105ndash1114 2011

[274] S B Kotsiantis ldquoDecision trees A recent overviewrdquo ArtificialIntelligence Review vol 39 no 4 pp 261ndash283 2013

[275] L Rokach and O Maimon Data mining with decision treestheory and applications World Scientific Data mining withdecision trees theory and applications 2014

[276] X-Z Zhu W Zhu and X-N Fan ldquoRough set methods infeature selection via submodular functionrdquo Soft Computing vol21 no 13 pp 3699ndash3711 2016

[277] H H Inbarani M Bagyamathi and A T Azar ldquoA novel hybridfeature selection method based on rough set and improvedharmony searchrdquo Neural Computing and Applications vol 26no 8 pp 1859ndash1880 2015

[278] G Beliakov DGomez S James JMontero and J T RodrıguezldquoApproaches to learning strictly-stable weights for data withmissing valuesrdquo Fuzzy Sets and Systems vol 325 pp 97ndash1132017

[279] S Jurado A Nebot F Mugica and M Mihaylov ldquoFuzzyinductive reasoning forecasting strategies able to cope withmissing data A smart grid applicationrdquoApplied Soft ComputingJournal vol 51 pp 225ndash238 2017

[280] A Paul J Sil and C D Mukhopadhyay ldquoGene selectionfor designing optimal fuzzy rule base classifier by estimatingmissing valuerdquoApplied Soft Computing Journal vol 55 pp 276ndash288 2017

[281] L Zhang W Lu X Liu W Pedrycz and C Zhong ldquoFuzzyc-means clustering of incomplete data based on probabilisticinformation granules of missing valuesrdquo Knowledge-Based Sys-tems vol 99 pp 51ndash70 2016

[282] H Shidpour C Da Cunha and A Bernard ldquoGroup multi-criteria design concept evaluation using combined rough set

theory and fuzzy set theoryrdquo Expert Systems with Applicationsvol 64 pp 633ndash644 2016

[283] C Bai DDhavale and J Sarkis ldquoComplex investment decisionsusing rough set and fuzzy c-means an example of investment ingreen supply chainsrdquo European Journal of Operational Researchvol 248 no 2 pp 507ndash521 2016

[284] M I Ali ldquoA note on soft sets rough soft sets and fuzzy soft setsrdquoApplied Soft Computing Journal vol 11 no 4 pp 3329ndash33322011

[285] X-Z Wang L-C Dong and J-H Yan ldquoMaximum ambiguity-based sample selection in fuzzy decision tree inductionrdquo IEEETransactions on Knowledge and Data Engineering vol 24 no 8pp 1491ndash1505 2012

[286] R Diao and Q Shen ldquoA harmony search based approach tohybrid fuzzy-rough rule inductionrdquo in Proceedings of the 2012IEEE International Conference on Fuzzy Systems June 2012

[287] J Błaszczynski R Słowinski and M Szeląg ldquoSequential cover-ing rule induction algorithm for variable consistency rough setapproachesrdquo Information Sciences vol 181 no 5 pp 987ndash10022011

[288] J Xu and L Zhao ldquoA multi-objective decision-making modelwith fuzzy rough coefficients and its application to the inventoryproblemrdquo Information Sciences An International Journal vol180 no 5 pp 679ndash696 2010

[289] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassification and predictionrdquoTheoretical Computer Science vol412 no 42 pp 5871ndash5884 2011

[290] Y Qu Q Shen NMac Parthalain C Shang andWWu ldquoFuzzysimilarity-based nearest-neighbour classification as alternativesto their fuzzy-rough parallelsrdquo International Journal of Approx-imate Reasoning vol 54 no 1 pp 184ndash195 2013

[291] M Sarkar ldquoFuzzy-rough nearest neighbor algorithms in clas-sificationrdquo Fuzzy Sets and Systems An International Journal inInformation Science and Engineering vol 158 no 19 pp 2134ndash2152 2007

[292] R Jensen and C Cornelis ldquoFuzzy-rough nearest neighbourclassificationrdquo Lecture Notes in Computer Science (includingsubseries Lecture Notes in Artificial Intelligence and Lecture Notesin Bioinformatics) vol 6499 pp 56ndash72 2011

[293] N Verbiest C Cornelis and R Jensen ldquoFuzzy rough positiveregion based nearest neighbour classificationrdquo in Proceedings ofthe 2012 IEEE International Conference on Fuzzy Systems June2012

[294] Z Zhang ldquoOn characterization of generalized interval type-2 fuzzy rough setsrdquo Information Sciences An InternationalJournal vol 219 pp 124ndash150 2013

[295] Z Zhang ldquoAn interval-valued intuitionistic fuzzy rough setmodelrdquo Fundamenta Informaticae vol 97 no 4 pp 471ndash4982009

[296] X Liu X Feng andW Pedrycz ldquoExtraction of fuzzy rules fromfuzzy decision trees An axiomatic fuzzy sets (AFS) approachrdquoData and Knowledge Engineering vol 84 pp 1ndash25 2013

[297] X-Z Wang J-H Zhai and S-X Lu ldquoInduction of multiplefuzzy decision trees based on rough set techniquerdquo InformationSciences An International Journal vol 178 no 16 pp 3188ndash32022008

[298] RM Rodrıguez L Martınez and F Herrera ldquoA group decisionmaking model dealing with comparative linguistic expressionsbased on hesitant fuzzy linguistic term setsrdquo Information Sci-ences vol 241 pp 28ndash42 2013

Complexity 33

[299] T Li D Ruan W Geert J Song and Y Xu ldquoA rough setsbased characteristic relation approach for dynamic attributegeneralization in data miningrdquo Knowledge-Based Systems vol20 no 5 pp 485ndash494 2007

[300] S P Tiwari and A K Srivastava ldquoFuzzy rough sets fuzzypreorders and fuzzy topologiesrdquo Fuzzy Sets and Systems AnInternational Journal in Information Science and Engineeringvol 210 pp 63ndash68 2013

[301] J Zhang T Li D Ruan and D Liu ldquoNeighborhood rough setsfor dynamic data miningrdquo International Journal of IntelligentSystems vol 27 no 4 pp 317ndash342 2012

[302] H Chen T Li C Luo S-J Horng and G Wang ldquoA Decision-Theoretic Rough Set Approach for Dynamic Data MiningrdquoIEEE Transactions on Fuzzy Systems vol 23 no 6 pp 1958ndash1970 2015

[303] M L Othman I Aris S M Abdullah M L Ali and M ROthman ldquoKnowledge discovery in distance relay event reporta comparative data-mining strategy of rough set theory withdecision treerdquo IEEE Transactions on Power Delivery vol 25 no4 pp 2264ndash2287 2010

[304] Y H Hung ldquoA neural network classifier with rough set-basedfeature selection to classify multiclass IC package productsrdquoAdvanced Engineering Informatics vol 23 no 3 pp 348ndash3572009

[305] Y Bi T Anderson and S McClean ldquoA rough set modelwith ontologies for discovering maximal association rules indocument collectionsrdquo Knowledge-Based Systems vol 16 no 5-6 pp 243ndash251 2003

[306] A Formica ldquoSemantic Web search based on rough sets andfuzzy formal concept analysisrdquo Knowledge-Based Systems vol26 pp 40ndash47 2012

[307] P Klinov and L J Mazlack ldquoFuzzy rough approach to handlingimprecision in Semantic Web ontologiesrdquo in Proceedings of theNAFIPS 2006 - 2006 Annual Meeting of the North AmericanFuzzy Information Processing Society pp 142ndash147 June 2006

[308] Q Hu D Yu and Z Xie ldquoInformation-preserving hybrid datareduction based on fuzzy-rough techniquesrdquo Pattern Recogni-tion Letters vol 27 no 5 pp 414ndash423 2006

[309] Q Shen and A Chouchoulas ldquoA rough-fuzzy approach forgenerating classification rulesrdquo Pattern Recognition vol 35 no11 pp 2425ndash2438 2002

[310] J-H Lee J R Anaraki C W Ahn and J An ldquoEfficientclassification system based on Fuzzy-Rough Feature Selectionand Multitree Genetic Programming for intension patternrecognition using brain signalrdquo Expert Systems with Applica-tions vol 42 no 3 pp 1644ndash1651 2015

[311] K Y Huang ldquoAn enhanced classification method comprisinga genetic algorithm rough set theory and a modified PBMF-index functionrdquo Applied Soft Computing Journal vol 12 no 1pp 46ndash63 2012

[312] C-H Cheng T-L Chen and L-Y Wei ldquoA hybrid model basedon rough sets theory and genetic algorithms for stock priceforecastingrdquo Information Sciences vol 180 no 9 pp 1610ndash16292010

[313] W-Y Liang and C-C Huang ldquoThe generic genetic algorithmincorporates with rough set theorymdashan application of the webservices compositionrdquo Expert Systems with Applications vol 36no 3 pp 5549ndash5556 2009

[314] Z Tao and J Xu ldquoA class of rough multiple objective pro-gramming and its application to solid transportation problemrdquoInformation Sciences An International Journal vol 188 pp 215ndash235 2012

[315] P Kundu M B Kar S Kar T Pal and M Maiti ldquoA solidtransportation model with product blending and parameters asrough variablesrdquo Soft Computing vol 21 no 9 pp 2297ndash23062017

[316] P Kumar S Gupta and B Bhasker ldquoAn upper approximationbased community detection algorithm for complex networksrdquoDecision Support Systems vol 96 pp 103ndash118 2017

[317] S-H Liao andH-K Chang ldquoA rough set-based association ruleapproach for a recommendation system for online consumersrdquoInformation Processing andManagement vol 52 no 6 pp 1142ndash1160 2016

[318] G A Montazer and S Yarmohammadi ldquoDetection of phishingattacks in Iranian e-banking using a fuzzy-rough hybrid sys-temrdquo Applied Soft Computing vol 35 pp 482ndash492 2015

[319] R Li and Z-O Wang ldquoMining classification rules using roughsets and neural networksrdquo European Journal of OperationalResearch vol 157 no 2 pp 439ndash448 2004

[320] X Pan S Zhang H Zhang X Na and X Li ldquoA variableprecision rough set approach to the remote sensing landusecover classificationrdquo Computers amp Geosciences vol 36 no12 pp 1466ndash1473 2010

[321] F Xie Y Lin andW Ren ldquoOptimizing model for land uselandcover retrieval from remote sensing imagery based on variableprecision rough setsrdquo Ecological Modelling vol 222 no 2 pp232ndash240 2011

[322] J Meng J Zhang R Li and Y Luan ldquoGene selection usingrough set based on neighborhood for the analysis of plant stressresponserdquo Applied Soft Computing Journal vol 25 pp 51ndash632014

[323] Y Chen Z Zhang J Zheng Y Ma and Y Xue ldquoGene selectionfor tumor classification using neighborhood rough sets andentropymeasuresrdquo Journal of Biomedical Informatics vol 67 pp59ndash68 2017

[324] P Maji and S Paul ldquoRough set based maximum relevance-maximum significance criterion and Gene selection frommicroarray datardquo International Journal of Approximate Reason-ing vol 52 no 3 pp 408ndash426 2011

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