Optimal Siting of Electric Vehicle Charging Stations Using Pythagorean Fuzzy VIKOR...

Research ArticleOptimal Siting of Electric Vehicle Charging Stations UsingPythagorean Fuzzy VIKOR Approach

Feng-Bao Cui12 Xiao-Yue You13 Hua Shi 4 and Hu-Chen Liu 4

1 School of Economics and Management Tongji University Shanghai 200092 China2Department of Economics amp Management Yibin University Yibin 644007 China3Institute for Manufacturing University of Cambridge Cambridge CB3 0FS UK4School of Management Shanghai University Shanghai 200444 China

Correspondence should be addressed to Hua Shi shihua1980shueducn

Received 13 November 2017 Revised 3 May 2018 Accepted 30 May 2018 Published 26 June 2018

Academic Editor Luiz H A Monteiro

Copyright copy 2018 Feng-Bao Cui et al This 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

Site selection for electric vehicle charging stations (EVCSs) is the process of determining the most suitable location amongalternatives for the construction of charging facilities for electric vehicles It can be regarded as a complex multicriteria decision-making (MCDM) problem requiring consideration of multiple conflicting criteria In the real world it is often hard or impossiblefor decision makers to estimate their preferences with exact numerical values Therefore Pythagorean fuzzy set theory hasbeen frequently used to handle imprecise data and vague expressions in practical decision-making problems In this papera Pythagorean fuzzy VIKOR (PF-VIKOR) approach is developed for solving the EVCS site selection problems in which theevaluations of alternatives are given as linguistic terms characterized by Pythagorean fuzzy values (PFVs) Particularly thegeneralized Pythagorean fuzzy ordered weighted standardized distance (GPFOWSD) operator is proposed to calculate the utilityand regret measures for ranking alternative sites Finally a practical example in Shanghai China is included to demonstrate theproposed EVCS sitting model and the advantages are highlighted by comparing the results with other relevant methods

1 Introduction

Due to the rapid economic development and the accelerationof urbanization energy shortage and environment pollutionhave become severe issues for the sustainable developmentof China Automobiles contribute 20ndash30 of the total pro-duction of greenhouse gases (GHGs) in China and thusthe reduction of GHGs is a very pressing problem forthe transportation sector [1] As a kind of environmentallyfriendly transportation electric vehicles are considered as apromising solution for the problems of energy consumptionand carbon emission [2] The central government is stronglymotivated to promote the adoption of electric vehicles tomaintain a healthy balance of urban mobility and energyconsumption and has set a goal of putting 5 million hybridand electric vehicles on the road by 2020 [3 4] In recent yearsmany strategies have been launched by local governmentsto accelerate electric vehicle marketization by for example

subsidizing manufacturers and buyers building chargingfacilities and offering tax breaks [5 6]

One of the factors that significantly influence the popu-larization and market acceptance of electric vehicles is accessto public charging infrastructure Because of the range limita-tion and resulting anxiety over the available range convenientand economic charging facilities can enhance the willingnessof consumers to buy electric vehicles The deployment ofpublic charging facilities is very important with regard toharmonious and sustainable development of electric vehiclesystems Site selection for electric vehicle charging stations(EVCSs) is the process of determining the most suitablelocation among alternatives for the construction of chargingfacilities for electric vehicles As a preliminary work itplays an important role in the transport planning and hassubstantial impact on the service quality and operationalefficiency of EVCSs [7] Therefore in recent years a great

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 9262067 12 pageshttpsdoiorg10115520189262067

2 Mathematical Problems in Engineering

deal of attention has been given for the determination of theoptimal location for EVCSs [3 7ndash10]

In practical EVCS site selection processes it is generallyhard to find an alternative that satisfies all criteria at thesame time so a good compromise solution is preferred Thisproblem may become more complex when multiple decisionmakers are involved each having a different perception onthe alternatives Therefore the optimal siting of EVCSs hasalways been a problemwhich can be effectively solved bymul-ticriteria decision-making (MCDM) methods The VIKOR(VIsekriterijumska optimizacija i KOmpromisno Resenje)method initially proposed by Opricovic and Tzeng [11] is anefficient tool to solve group decision-making problems withcontradictory and noncommensurable criteria It assumesthat compromising is adequate for conflict resolution thedecision maker wants a solution which is the closest to theideal and the alternatives are ordered based on all predefinedcriteria [12 13] This technique is a helpful tool in thesituations where a decision maker is not able to indicatepreferences among alternatives that may result in varied con-sequences Because of its characteristics and competenciesthe VIKOR method is a promising tool to find the optimallocation of EVCSs

Normally the techniques such as initial interview fieldinvestigation and programming (optimization) models wereused for the optimal location of EVCSs [7] However withthe increasing complexity of EVCS site selection problemsdecisionmakers often need to consider multiple criteria suchas the effect on ecological environment the investment payoffperiod and the attitude of local residents to make decisionsThere are also some situations when the assessments ofalternatives must cope with the vagueness of establishedcriteria and the development of a fuzzy MCDM method isneeded to handle either qualitative or incomplete data [2 78] As a generalization of intuitionistic fuzzy sets [14] thePythagorean fuzzy sets (PFSs) were introduced by Yager andAbbasov [15] The PFSs are also characterized by a member-ship degree and a nonmembership degree whose square sumis less than or equal to 1 but the sum is not required to be lessthan one Consequently the theory of PFSs can depict moreimprecise and ambiguous information in solving MCDMproblems [16ndash18] In many real circumstances particularlyin the process of group decision-making under uncertaintythe judgments or preferences provided by decision makersmay be appropriately expressed in Pythagorean fuzzy values(PFVs) [19] Thus PFSs can be very useful to manage thesubjective evaluations of domain experts in the EVCS siteselection

Based on above discussions this paper presents aPythagorean fuzzy VIKOR (PF-VIKOR) method to selectthe optimal site of EVCSs under Pythagorean fuzzy envi-ronment Specifically the evaluations of alternatives againsteach criterion are treated as linguistic terms which can bedenoted by PFVsThe Pythagorean fuzzy weighted averaging(PFWA) operator [20] emphasizing the individual influenceis employed to aggregate all decision makersrsquo opinions intogroup assessments Particularly the generalized Pythagoreanfuzzy ordered weighted standardized distance (GPFOWSD)operator is proposed to calculate the utility and regret

measures of the PF-VIKOR The new model can not onlyinclude the attitudinal character of a decision maker for thesite selection of EVCSs but also parameterize the results fromthe minimum to the maximum according to the decisionmakerrsquos interests Thus it is able to provide a wide range ofsituations according to the attitude taken by a decision makerin the particular application considered

The rest of this paper is outlined as follows in Section 2a review of the existing literature related to this study isincluded In Section 3 somebasic concepts related to PFSs arereviewed and theGPFOWSDoperator is developed Section 4provides the PF-VIKORmethod to group EVCS site selectionA numerical example is provided in Section 5 to illustrate theproposed approach and a comparative analysis is conductedto display the advantages of the new EVCS site selectionmodel Finally conclusions of this article are presented inSection 6

2 Literature Review

21 Application of VIKOR Method Recently the VIKORmethod has been successfully utilized by scholars to handlevarious decision-making problems For example Yalcın andUnlu [21] used VIKOR and CRiteria Importance ThroughIntercriteria Correlation (CRITIC) methods for the multicri-teria performance evaluation of initial public offering firmsWang et al [22] presented an integrated model based onVIKOR and entropy weight methods for the risk evaluationof construction project under picture fuzzy environmentTavana et al [23] constructed an extended VIKOR approachthat accounts for differences in the risk attitudes of decisionmakers when ranking stochastic alternatives Sennaroglu andVarlik Celebi [24] solved the location selection problem fora military airport by combining analytic hierarchy process(AHP) and VIKOR methods Gul et al [25] proposed amodeling framework incorporating fuzzy AHP with fuzzyVIKOR for occupational health and safety risk assess-ment Shojaei et al [26] proposed an integration methodusing Taguchi loss function best-worst method and VIKORtechnique to evaluate and rank airports and Gupta [27]evaluated the service quality of airline industry using ahybrid approach consisting of best-worstmethod andVIKORmethod In [28] an environmentally friendly decision-making model using decision-making trial and evaluationlaboratory- (DEMATEL-) based analytical network process(ANP) (DANP) interval uncertainty and VIKOR methodwas presented for the reliability-based product optimizationIn [29] a compromising decision-making method based oninterval-valued Pythagorean fuzzy sets and VIKOR methodwas developed and applied to decision analysis for hospital-based post-acute care In [30] the authors employed an inte-grated fuzzy AHP-VIKOR framework for multi-tier sustain-able global supplier selection Besides a systematic review ofthe literature on the VIKOR method and its applications canbe found in [31 32]

22 Application of PFSs The PFSs have received wide atten-tion in recent years and many researchers have applied it toaddress a variety of real-world decision-making problems

Mathematical Problems in Engineering 3

For instance Xue et al [33] proposed a Pythagorean fuzzylinear programming technique formultidimensional analysisof preference (LINMAP) method based on entropy theoryfor railway project investment decision-making Liang etal [34] reported a method of three-way decisions-basedideal solutions in the Pythagorean fuzzy information sys-tem and used the technique for order preference by sim-ilarity to ideal solution (TOPSIS) method to estimate theconditional probability Ilbahar et al [35] constructed anintegrated risk assessment approach for occupational healthand safety using Fine Kinney Pythagorean fuzzy AHP andfuzzy inference system Chen [36] suggested a remotenessindex-based VIKOR method for multiple criteria decisionanalysis involving Pythagorean fuzzy information An agent-based Pythagorean fuzzy model was developed by Balogluand Demir [37] for demand analysis in environments withincomplete information A closeness index-based QUAL-IFLEX method was proposed by Zhang [38] to addresshierarchical multicriteria decision-making problems withinthe Pythagorean fuzzy context Ren et al [39] introduced amodified TODIM (an acronym in Portuguese of interactiveand multiple criteria decision-making) method and Zhangand Xu [19] proposed an extended TOPSIS approach to dealwith the Pythagorean fuzzy MCDM problems In additiona variety of aggregation operators such as the Pythagoreanfuzzy induced ordered weighted averaging weighted averageoperator [40] the Pythagorean fuzzy Maclaurin symmetricmean operators [41] the Pythagorean fuzzy power aggrega-tion operators [42] the Pythagorean fuzzy Bonferroni meanaggregation operator [43] and the probabilistic Pythagoreanfuzzy aggregation operators [44] were developed for complexdecision-making in the Pythagorean fuzzy environment

23 EVCS Site Selection The optimal location of EVCSsis a hot topic which has received much more attention inrecent years To maximize the demand coverage Yang [45]developed a user-choice model for locating congested fastcharging stations and deploying chargers in a stochasticenvironment He et al [46] presented a bi-level program-ming model to location planning of charging stations withthe consideration of EVsrsquo driving range Guo et al [47]established a bi-level integer programming model to solvethe battery charging station location problem consideringimpact of usersrsquo range anxiety and distance convenienceTu et al [9] addressed the location problem of electric taxicharging stations by presenting a spatialndashtemporal demandcoverage method Shahraki et al [3] selected the optimallocations of electric public charging stations by formulatingan optimization model based on vehicle travel behaviors Onthe other hand Liu et al [48] proposed an integrated MCDMapproach using grey decision-making trial and evaluationlaboratory (DEMATEL) and uncertain linguistic MULTI-MOORA (multiobjective optimization by a ratio analysis plusthe full multiplicative form) for finding the best locationof EVCSs Zhao and Li [2] employed a fuzzy grey relationanalysis- (GRA-) VIKOR method and Guo and Zhao [7]utilized a fuzzy TOPSIS method for optimal siting of EVCSsfrom a sustainability perspective Wu et al [49] built an

EVCS site selection approach for residential communitiesbased on triangular intuitionistic fuzzy numbers and VIKORmethod

After analyzing the literature it can be concluded thatthe majority of existing studies related to the site selection ofEVCSs are concentrated on multiobjective decision-making(MODM) methods and only limited research has dealt withthe problems using MCDM methods However the MODMmethods can only account for quantitative factors and arenot capable of modeling important qualitative factors [27] In addition the VIKOR method has been successfullyemployed in sitting EVCSs and has demonstrated satisfactoryresults [2 49] but no study has dealt with the EVCS siteselection in the Pythagorean fuzzy environment Thereforewe intend to develop a new MCDM model in this study toperform the EVCS site selection by combining Pythagoreanfuzzy sets and VIKOR method in order to capture bothquantitative and qualitative criteria and model imprecisionand vagueness of assessment information given by decisionmakers

3 Preliminaries

31 Pythagorean Fuzzy Sets The concept of PFSs was initiallyintroduced by Yager [35] by extending intuitionistic fuzzysets [14] and the general mathematical form of PFSs wasproposed by Zhang and Xu [19] Next the basic definitionsand concepts related to PFSs are given

Definition 1 Let 119883 be a fixed nonempty set A PFS 119875 in 119883 isdefined as

119875 = ⟨119909 120583119875 (119909) ]119875 (119909)⟩ | 119909 isin 119883 (1)

which is characterized by a membership function 120583119875 119883 rarr[0 1] and a nonmembership function ]119875 119883 rarr [0 1] andsatisfies the condition that 0 le (120583119875(119909))2 + (]119875(119909))2 le 1 for all119909 isin 119883 The numbers 120583119875 and ]119875 are the membership degreeand the nonmembership degree of the element 119909 to the set 119875respectively

For each PFS 119875 in 119883 the function 120587119875(119909) =radic1 minus (120583119875(119909))2 minus (]119875(119909))2 is called the hesitation degree(or Pythagorean index [38]) of the element 119909 isin 119883 to the set119875 For a PFS 119875 in119883 the pair 119901 = (120583119901(119909) ]119901(119909)) is referred toas a Pythagorean fuzzy value (PFV) [19] and each PFV canbe denoted by 119901 = (120583119901 ]119901) for convenienceDefinition 2 For any two PFVs 1199011 = (1205831199011 ]1199011) and 1199012 =(1205831199012 ]1199012) the basic mathematical operations of PFVs aredefined as follows [19]

(1) 1199011 oplus 1199012 = (radic(1205831199011)2 + (1205831199012)2 minus (1205831199011)2(1205831199012)2 V1199011V1199012)(2) 1199011 otimes 1199012 = (12058311990111205831199012 radic(V1199011)2 + (V1199012)2 minus (V1199011)2(V1199012)2)


(3) 1205821199011 = (radic1 minus (1 minus (1205831199011)2)120582 (V1199011)120582) 120582 gt 0(4) 1199011205821 = ((1205831199011)120582 radic1 minus (1 minus (V1199011)2)120582) 120582 gt 0

Definition 3 Let Φ be the set of all PFVs in 119883 The scorefunction of a PFV 119901 = (120583119901 ]119901) is represented as follows [50]

119878 (119901) = 12 (1 + (120583119901)2 minus (V119901)2) (2)

and the accuracy function of a PFV 119901 = (120583119901 ]119901) is defined bythe following [51]

119867(119901) = (120583119901)2 + (V119901)2 (3)

where 119878(119901) isin [0 1] and119867(119901) isin [0 1]In line with the score function 119878 and the accuracy

function119867 Wu andWei [50] gave the following comparisonlaws of PFVs

Definition 4 Supposing there are two PFVs 1199011 = (1205831199011 ]1199011)and 1199012 = (1205831199012 ]1199012) then

(1) if 119878(1199011) gt 119878(1199012) then 1199011 gt 1199012(2) if 119878(1199011) = 119878(1199012) and119867(1199011) gt 119867(1199012) then 1199011 gt 1199012(3) if 119878(1199011) = 119878(1199012) and119867(1199011) = 119867(1199012) then 1199011 = 1199012Zhang and Xu [19] further proposed the Hamming

distance measure for Pythagorean fuzzy decision-making

Definition 5 (see [19]) Let 1199011 = (1205831199011 ]1199011) and 1199012 = (1205831199012 ]1199012)be two PFVs in Φ The Hamming distance between them iscomputed by

119889119867 (1199011 1199012) = 12 (100381610038161003816100381610038161003816(1205831199011)2 minus (1205831199012)2100381610038161003816100381610038161003816 + 100381610038161003816100381610038161003816(V1199011)2 minus (V1199012)2100381610038161003816100381610038161003816+ 100381610038161003816100381610038161003816(1205871199011)2 minus (1205871199012)2100381610038161003816100381610038161003816)

(4)

Based on the basic operational rules of PFVs Zhang[20] developed the Pythagorean fuzzy weighted averaging(PFWA) operator as follows

Definition 6 (see [20]) Suppose 119901119894 = (120583119901119894 ]119901119894) (119894 =1 2 119899) is a collection of PFVs in Φ Then the PFWAoperator is defined as follows

119875119865119882119860(1199011 1199012 119901119899) = 119899⨁119894=1

119908119894119901119894= (radic1 minus 119899prod

119894=1

(1 minus (120583119901119894)2)119908119894 119899prod119894=1

(V119901119894)119908119894) (5)

where 119908 = (1199081 1199082 119908119899)119879 is the associated weights of119901119894 (119894 = 1 2 119899) satisfying 119908119894 isin [0 1] (119894 = 1 2 119899) andsum119899119894=1119908119894 = 1

32 The GPFOWSD Operator Motivated by the gener-alized ordered weighted averaging standardized distance(GOWASD) operator [52] we develop a generalized Py-thagorean fuzzy ordered weighted standardized distance(GPFOWSD) operator for the VIKOR method Let lowast =119901lowast1 119901lowast2 119901lowast119899 minus = 119901minus1 119901minus2 119901minus119899 and 119894 = 1199031198941 1199031198942 119903119894119899 be three sets of PFVs then we can define theGPFOWSD as follows

Definition 7 An GPFOWSD operator of dimension 119899 is amapping GPFOWSD Φ119899 times Φ119899 times Φ119899 rarr 119877 that has anassociated weighting vector 120596 = (1205961 1205962 120596119899)119879 with 120596119896 isin[0 1] and Σ119899119896=1120596119896 = 1 such that

GPFOWSD (⟨119901lowast1 119901minus1 1199031198941⟩ ⟨119901lowast1 119901minus1 119903119894119899⟩)= ( 119899sum119896=1

120596119896119889120582119896)1120582 120582 = 0 (6)

where 119889119896 represents the kth largest of the standardizedPythagorean fuzzy distance 119889(119901lowast119895 119903119894119895)119889(119901lowast119895 119901minus119895 ) and 119901lowast119895 and119901minus119895 are the Pythagorean fuzzy positive ideal solution (PFPIS)and the Pythagorean fuzzy negative ideal solution (PFNIS) ofthe jth criterion 119903119894119895 is the assessment of ith alternative withregard to C119895 119894 = 1 2 119898 119895 = 1 2 119899

Note that the GPFOWSD operator is commutativemonotonic idempotent and bounded which can be proveneasily and omitted here In addition by analyzing the weight-ing vector120596and the parameter 120582 in the GPFOWSD operatordifferent types of Pythagorean fuzzy distance operators canbe acquired

Remark 8 If 120582 = 1 then the GPFOWSD operator is reducedto the Pythagorean fuzzy ordered weighted Hamming stan-dardized distance (PFOWHSD) operator

PFOWHSD (⟨119901lowast1 119901minus1 1199031198941⟩ ⟨119901lowast1 119901minus1 119903119894119899⟩)= 119899sum119896=1

120596119896119889119896 (7)

where 119889119896 represents the kth largest of the standardizedPythagorean fuzzy distance 119889(119901lowast119895 119903119894119895)119889(119901lowast119895 119901minus119895 ) Note thatif 120596119896 = 1119899 for all k we get the Pythagorean fuzzynormalizedHamming standardized distance (PFNHSD)ThePythagorean fuzzyweightedHamming standardized distance(PFWHSD) is obtained if the position of j is the same as theordered position of k

Remark 9 If 120582 = 2 the GPFOWSDoperator is reduced to thePythagorean fuzzy ordered weighted Euclidean standardizeddistance (IFOWESD) operator

PFOWESD (⟨119901lowast1 119901minus1 1199031198941⟩ ⟨119901lowast1 119901minus1 119903119894119899⟩)= ( 119899sum119896=1

1205961198961198892119896)12 (8)


where 119889119896 represents the kth largest of the standardizedPythagorean fuzzy distance 119889(119901lowast119895 119903119894119895)119889(119901lowast119895 119901minus119895 ) Note thatif 120596119896 = 1119899 for all k we get the Pythagorean fuzzynormalized Euclidean standardized distance (PFNESD)ThePythagorean fuzzy weighted Euclidean standardized distance(PFWESD) is obtained if the position of j is the same as theordered position of k

Remark 10 If 120582 rarr 0 then the GPFOWSD operator isreduced to the Pythagorean fuzzy ordered weighted geomet-ric standardized distance (PFOWGSD) operator

PFOWGSD (⟨119901lowast1 119901minus1 1199031198941⟩ ⟨119901lowast1 119901minus1 119903119894119899⟩)= 119899prod119896=1

119889120596119896119896 (9)

where 119889119896 represents the kth largest of the standardizedPythagorean fuzzy distance 119889(119901lowast119895 119903119894119895)119889(119901lowast119895 119901minus119895 ) Note thatif 120596119896 = 1119899 for all k we get the Pythagorean fuzzynormalized geometric standardized distance (PFNGSD)ThePythagorean fuzzy weighted geometric standardized distance(PFWGD) is obtained if the position of j is the same as theordered position of k Note also that the PFOWGSD can onlybe used when all the individual standardized distances aredifferent from 0 That is when 119889(119891lowast119895 119903119894119895)119889(119891lowast119895 119891minus119895 ) = 0 forall j

Using a similar methodology as for the GOWASD [52]operator numerous other families of GPFOWSD operatorscan be proposed For instance we could define the step-PFOWSD operator the window-PFOWSD the Olympic-PFOWSD the median-PFOWSD the centered-PFOWSDand the non-monotonic-PFOWSD

4 The Proposed EVCS Site Selection Method

In this section we extend the VIKOR method to thePythagorean fuzzy environment for finding the optimallocation of EVCSs Inmany practical situations the criteria ofalternative sites are not easy to be precisely evaluated becauseof the increasing complexity and the lack of knowledgeor data As such in this paper linguistic terms are usedby decision makers to express their subjective judgmentson EVCS locations and the individual evaluation grade isdefined as a PFV Similar to [36] the linguistic terms can berepresented by PFVs as presented in Table 1 In practice themembership functions for linguistic terms can be estimatedaccording to historical data or the questionnaire answered bydecision makers

Assuming that an EVCS site selection problem has ldecision makers119863119872119896 (119896 = 1 2 119897)m alternatives 119860 119894 (119894 =1 2 119898) and n evaluation criteria 119862119895 (119895 = 1 2 119899)Each decision maker DMk is given a weight 119908119896 gt 0 (119896 =1 2 119897) satisfying sum119897119896=1119908119896 = 1 to reflect hisher relativeimportance in the EVCS site selection process Based uponthese assumptions the detailed steps of the Pythagoreanfuzzy VIKOR (PF-VIKOR) are described as follows

Table 1 Linguistic terms for rating alternatives

Linguistic terms PFVsVery Low (VL) (015 085)Low (L) (025 075)Moderately Low (ML) (035 065)Medium (M) (050 045)Moderately High (MH) (065 035)High (H) (075 025)Very High (VH) (085 015)

Step 1 Pull the decision makersrsquo opinions to construct aPythagorean fuzzy assessment matrix

In the EVCS site selection process all the participatedexpertsrsquo judgments need to bemerged into group assessmentsto construct an aggregated Pythagorean fuzzy assessmentmatrix Let 119903119896119894119895 = (120583119896119894119895 V119896119894119895) be the PFV provided by DMk onthe assessment of Ai in relation to Cj Then the aggregatedPythagorean fuzzy ratings (119903119894119895) of alternatives with respect toeach criterion are calculated by using the PFWA operator

119903119894119895 = PFWA (1199031119894119895 1199032119894119895 119903119897119894119895) = 119897⨁119896=1

120582119896119903119896119894119895

= (radic1 minus 119897prod119896=1

(1 minus (120583119896119894119895)2)119908119896 119897prod119896=1

(V119896119894119895)119908119896) 119894 = 1 2 119898 119895 = 1 2 119899

(10)

Hence an EVCS site selection problem can be conciselyrepresented in a matrix format as follows

= [[[[[[[

11990311 11990312 sdot sdot sdot 119903111989911990321 11990322 sdot sdot sdot 1199032119899 sdot sdot sdot 1199031198981 1199031198982 sdot sdot sdot 119903119898119899

]]]]]]] (11)

where 119903119894119895 = (120583119894119895 V119894119895) is an element of the aggregatedPythagorean fuzzy assessment matrix Step 2 Determine the PFPIS 119901lowast119895 = (120583lowast119895 Vlowast119895 ) and the PFNIS119901minus119895 = (120583minus119895 Vminus119895 ) of all criteria ratings by

119901lowast119895 = max119894

119903119894119895 for benefit criteria

min119894

119903119894119895 for cost criteria119895 = 1 2 119899

(12)


119901minus119895 = min119894


max119894


(13)

Step 3 Compute the values of 119878119894 and 119877119894 as follows119878119894 = GPFOWSD (⟨119901lowast1 119901minus1 1199031198941⟩ ⟨119901lowast1 119901minus1 119903119894119899⟩)= ( 119899sum119896=1

120596119896119889120582119896)1120582 119894 = 1 2 119898 (14)

119877119894 = (max119896

(120596119896119889120582119896))1120582 119894 = 1 2 119898 (15)

where120596119896 are the ordered weights of criteria representing therelative importance of their ordered positions Many differentmethods have beenproposed in the literature for determiningthe ordered weighted average (OWA) weights [53] thatcan also be implemented for the GIFOWSD operator It isworth noting that it is possible to consider a wide range ofGPFOWSD operators such as those presented in Section 32

Step 4 Compute the values 119876119894 by the relation119876119894 = V

119878119894 minus 119878lowast119878minus minus 119878lowast + (1 minus V) 119877119894 minus 119877lowast119877minus minus 119877lowast 119894 = 1 2 119898 (16)

where 119878lowast = min119894119878119894 119878minus = max119894119878119894 119877lowast = min119894119877119894 119877minus =max119894119877119894 V is introduced as a weight of the maximum grouputility whereas 1-V is the weight of the individual regret Inthis paper the value of V is taken as 05

Step 5 Rank the alternative sites based on the values of 119878 119877and 119876 in increasing order The results are three ranking lists

Step 6 Propose a compromise solution The alternative 119860(1)with the minimum 119876 value is considered to be a compromisesolution for the given criteria weights if the following twoconditions are satisfied

(C1) Acceptable advantage 119876(119860(2)) minus119876(119860(1)) ge 1(119898minus 1)where 119860(2) is in the second place of the alternativesranked by 119876

(C2) Acceptable stability the alternative 119860(1) must also bethe best according to 119878 orand 119877 This compromisesolution is stable within the EVCS site selectionprocess which could be ldquovoting by majority rulerdquo(V gt 05) or ldquoby consensusrdquo V asymp 05 or ldquowith vetordquo(V lt 05)

When only one of the two conditions is not satisfieda set of compromise solutions can be proposed which arecomposed of

(i) alternatives 119860(1) and 119860(2) if the condition (C2) is notsatisfied

(ii) alternatives 119860(1) 119860(2) 119860(119872) if the condition (C1)is not satisfied 119860(119872) is calculated using the relation119876(119860(119872)) minus 119876(119860(1)) lt 1(119898 minus 1) for maximum119872

Figure 1 Geographical locations of the alternative sites

5 Illustrative Example

In this section an empirical study conducted in ShanghaiChina [48] is provided to illustrate the applicability andefficacy of the proposed EVCS site selection model

51 Background Description Shanghai is one of the fastestdeveloping cities in China and because of rapidly economydevelopment vehicle demand is rising dramatically In 2016the number of cars in Shanghai reached 322 million rankingthe fourth in China Similar to others cities in Chinaair pollution is a growing problem in Shanghai HenceShanghai government is endeavoring to promote sustain-able development of the EV industry Currently a Chineseelectricity company needs to construct a charging stationfor EVs in Shanghai based on the companyrsquos developmentstrategy and market requirements After initial screeningfour sites located in Minghang district (A1) Jiading district(A2) Baoshan district (A3) and Pudong district (A4) aredetermined as the alternative sites as shown in Figure 1 Anexpert committee consisting of five decisionmakers (denotedas DM1DM2 DM5) has been formed to conduct theassessment and select the most suitable site for the EVCSThese experts are authorities in the areas of engineeringeconomy environment electrical power system and trans-portation system

Generally it is needed to consider various criteria todetermine the optimal siting of EVCSs According to aliterature review and expert interviews four dimensionstogether with their criteria are taken into account for


Figure 2 Dimensions and related criteria for EVCS site selection

Table 2 Linguistic assessed information of the alternative sites

Decision makers Alternatives CriteriaC1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

DM1 A1 H H H H H H M H H L M MHA2 H MH H VH M H M MH M ML ML MA3 MH MH VH H M VH M H VH L MH HA4 VH H VH H H M MH H M VL M MH

DM2 A1 VH H H H H H MH H MH L M MHA2 VH H H VH MH H M MH M ML ML MA3 H MH VH VH M VH M VH MH L MH HA4 VH MH VH H VH M M H M VL M MH

DM3 A1 H MH H H H MH M H H ML M MA2 H MH VH VH M H M M ML L M MA3 H MH VH VH MH VH MH H VH L MH VHA4 VH H H H H MH M H M VL MH H

DM4 A1 VH H H MH MH H M H H L M HA2 VH MH MH VH M H MH MH M ML ML MA3 MH MH H VH MH VH M H VH VL M MA4 VH H VH VH H M M H M VL M MH

DM5 A1 VH MH H H H H M H MH L M MHA2 H H H VH MH H M M M ML ML MA3 H MH VH H M VH M VH VH L MH HA4 VH H VH H MH M MH VH M VL M H

evaluating the alternative sites comprehensively (see Fig-ure 2) Given the difficulty in precisely assessing thesecriteria the five experts are assumed to evaluate themby using the linguistic terms defined in Table 1 After-wards the linguistic evaluations of the decision makers forthe four alternatives are obtained as shown in Table 2

The five decision makers from different organizations aresupposed to be of different importance considering theirdifferent academic backgrounds and domain knowledgeHence they are assigned the following relative weights015 020 025 025 and 015 in the EVCS site selectionprocess


Table 3 Aggregated Pythagorean fuzzy assessment matrix C1 C2 C3 C4 C5 C6

A1 (0817 0184) (0715 0286) (0750 0250) (0729 0272) (0729 0272) (0729 0272)A2 (0802 0199) (0690 0311) (0763 0239) (0850 0150) (0562 0412) (0750 0250)A3 (0715 0286) (0650 0350) (0830 0170) (0826 0175) (0585 0397) (0850 0150)A4 (0850 0150) (0733 0267) (0830 0170) (0781 0220) (0764 0237) (0545 0423)

C7 C8 C9 C10 C11 C12

A1 (0537 0428) (0750 0250) (0720 0281) (0279 0724) (0500 0450) (0652 0343)A2 (0545 0423) (0599 0387) (0469 0493) (0328 0674) (0395 0593) (0500 0450)A3 (0545 0423) (0792 0209) (0824 0178) (0229 0774) (0619 0373) (0744 0255)A4 (0554 0417) (0769 0232) (0500 0450) (0150 0850) (0545 0423) (0695 0306)

52 Application and Results Next we use the PF-VIKORapproach to select the optimal site for the EVCS whichinvolves the following steps

Step 1 After converting the linguistic evaluations of decisionmakers into PFVs according to Table 1 the aggregatedPythagorean fuzzy assessment matrix = [119903119894119895]4times12 is formedby utilizing (10) The calculated results are presented inTable 3

Step 2 The benefit criteria are C3 C4 C6 C8 C9 C11 C12and the cost criteria are C1 C2 C5 C7 C10 Thus the PFPISand the PFNIS of the twelve criteria ratings are determinedas follows 119891lowast1 = (0715 0286)

119891lowast2 = (0650 0350) 119891lowast3 = (0830 0170) 119891lowast4 = (0850 0150) 119891lowast5 = (0562 0412) 119891lowast6 = (0850 0150) 119891lowast7 = (0537 0428) 119891lowast8 = (0792 0209) 119891lowast9 = (0824 0178) 119891lowast10 = (0150 0850) 119891lowast11 = (0619 0373) 119891lowast12 = (0744 0255) 119891minus1 = (0850 0150) 119891minus2 = (0733 0267) 119891minus3 = (0750 0250) 119891minus4 = (0729 0272) 119891minus5 = (0764 0237)

119891minus6 = (0545 0423) 119891minus7 = (0554 0417) 119891minus8 = (0599 0387) 119891minus9 = (0469 0493) 119891minus10 = (0328 0674) 119891minus11 = (0395 0593) 119891minus12 = (0500 0450)

(17)

Steps 3 and 4 In this example we use the PFNHSD thePFWHSD the PFOWHSD the PFNESD the PFWESDand the PFOWESD operators in the PF-VIKOR methodwhile assuming that the OWA weights are 120596 = (0035300538 00752 00968 01144 01245 01245 01144 0096800752 00538 00353) [53] According to (14)-(16) the resultsobtained are listed in Table 4

Step 5 Based on the values of S R and Q the rankings of thefour alternatives are obtained as shown in Table 5 It is clearthat A3 is the most appropriate alternative for all the casesfollowed by A1 A2 and A4

It should be noted that depending on the particular typeof the distance operator used the ordering of the alternativesmay be dissimilar thus leading to different decisions There-fore the electricity company can properly select the desirableEVCS site according to actual needs But in this example itseems clear thatA3 is the optimal choiceTherefore the EVCSsite in Baoshan district should be selected as the best EVCSsite in this case study

53 Comparative Study To demonstrate the effectiveness ofthe proposed PF-VIKOR approach we use the data in theabove example to analyze some existing EVCS site selectionmethods such as the fuzzy GRA-VIKOR [2] and the fuzzyTOPSIS [7] methods In addition we extend the TOPSISmethod with PFSs and use the Pythagorean Fuzzy TOPSIS(PF-TOPSIS) for solving the same case study The rankingresults of the four alternative sites derived by using thesemethods are summarized in Table 6 From the results in


Table 4 Aggregated results

Distance operator A1 A2 A3 A4

PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986

Table 5 Rankings of the alternatives by the PF-VIKORmethod

Distance operator Ranking Distance operator RankingPFNHSD 1198603 ≻ 1198601 ≻ 1198604 ≻ 1198602 PFNESD 1198603 ≻ 1198601 ≻ 1198604 ≻ 1198602PFWHSD 1198603 ≻ 1198601 ≻ 1198602 ≻ 1198604 PFWESD 1198603 ≻ 1198601 ≻ 1198602 ≻ 1198604PFOWHSD 1198603 ≻ 1198601 ≻ 1198604 ≻ 1198602 PFOWESD 1198603 ≻ 1198601 ≻ 1198604 ≻ 1198602

Table 6 Ranking comparison

Alternatives Fuzzy GRA-VIKOR Fuzzy TOPSIS PF-TOPSISS R Q Ranking CC Ranking CC Ranking

A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4

Table 6 the advantages of the proposed PF-VIKOR modelover other EVCS site selection methods can be identified

As we can see the top two alternatives obtained fromthe proposed approach and the three compared methodsare exactly the same ie A3 and A1 Particularly when thePFWHSD and the PFWESD operators are used our prioriti-zation of the alternatives is in accordance with the rankingsyielded by the fuzzy GRA-VIKOR the fuzzy TOPSIS and thePF-TPOSIS methods Besides the same EVCS site selectionexample has been investigated by Liu et al [48] and theresult showed that the site in Baoshan district (A3) is themost suitable location These demonstrate the validity of theproposed EVCS siting approach

On the other hand there are some differences in thepriority orders of alternatives if other types of distance oper-ators are adopted in the proposed approach The divergencesmainly result from different characteristics between the listed

methods and the presented PF-VIKOR approach First boththe fuzzy GRA-VIKOR and the fuzzy TOPSIS methodsadopt fuzzy sets to depict the performance assessments ofalternatives provided by the decision makers However thefuzzy set theory considering only a membership function isnot able to model imprecision and vagueness of assessmentinformation in detail and comprehensively Second the rank-ings of alternative sites are determined based on the GRA-VIKOR and the TOPSIS in the three compared methods Butthe TOPSIS method introduces two reference points withoutconsidering the relative importance of the distances fromthese points Moreover the calculation complexity of theGRA-VIKOR method is relatively higher than the VIKORmethod used in this study That is the proposed approach isable to generate identical results in less time complexity

Therefore from the comparative analysis it can be con-cluded that the proposed approach is more flexible and useful


to deal with EVCS site selection problems and can providemore information for the sitting decision-making Comparedwith other EVCS location models the PF-VIKOR approachprovided in this study has the following attractions

(i) Based on PFSs the vagueness and complex uncer-tainty of performance assessments can be effectivelyhandled The proposed method gives experts theadditional ability to represent imprecise knowledgeand can address EVCS site selection problems in amore flexible way

(ii) The attitudinal character of a decision maker can bereflected by using the GPFOWSD operator in theselection process of EVCSs As a result we are able tounderestimate or overestimate the results accordingto the desired degree of optimism

(iii) We can get a complete picture of an EVCS siteselection problem by considering a wide range ofdistance operators Hence the decision maker is ableto make decisions taking different scenarios intoconsideration and select the one that better fits his orher interests

(iv) The PF-VIKOR method introduced a ranking indexbased on the particular measure of closeness tothe ideal solution which is an aggregation of allcriteria and their importance and a balance betweentotal and individual satisfaction Therefore a morereasonable and reliable ranking of alternatives can bederived according to the basic principle of the VIKORmethod

6 Conclusions

Vehicle electrification is a promising approach to addresspeak oil and air pollution problems As the energy providerof electric vehicles the construction of EVCSs is picking upspeed to ensure the synergetic development of the technologyThe selection of the best site for EVCSs which considers mul-tiple criteria exhibiting vagueness and imprecision can beregarded as a complicated MCDM problem In this researchan extended VIKOR method called PF-VILOR is proposedfor the optimal siting of EVCSs under Pythagorean fuzzysetting This model is easy to implement and consistent withhuman recognition In the performance evaluation processthe rating values of alternatives are treated as linguistic termsexpressed by PFVs The PFWA operator is employed tofuse individual opinions of decision makers into collectiveassessmentsThen the rank orders of alternatives are obtainedby utilizing an improved VILOR method in which the SR and Q values of each alternative are calculated basedon the GIFOWSD operator Finally the effectiveness andadvantages of our proposed EVCS site selection approach aredemonstrated by a case study conducted in Shanghai China

In future research it is a meaningful topic to extendour approach to the interval-valued Pythagorean Flow [54]and the Pythagorean uncertain linguistic [55] environmentsAlso as we can see with the development of cloud modeltheory and hesitant fuzzy linguistic term sets in the future

our work should be well attached with such new technologiesto explore new application areas in other decision-makingproblems

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was partially supported by the National NaturalScience Foundation of China (nos 61773250 and 71671125)the Shanghai Shuguang Plan Project (no 15SG44) and theShanghai Youth Top-Notch Talent Development Program

References

[1] Y Xue J You X Liang andH-C Liu ldquoAdopting strategic nichemanagement to evaluate EV demonstration projects in ChinardquoSustainability vol 8 no 2 2016

[2] H Zhao and N Li ldquoOptimal siting of charging stations forelectric vehicles based on fuzzyDelphi andhybridmulti-criteriadecision making approaches from an extended sustainabilityperspectiverdquo Energies vol 9 no 4 2016

[3] N Shahraki H Cai M Turkay and M Xu ldquoOptimal locationsof electric public charging stations using real world vehicletravel patternsrdquo Transportation Research Part D Transport andEnvironment vol 41 pp 165ndash176 2015

[4] H-C Liu X-Y You Y-X Xue and X Luan ldquoExploring criticalfactors influencing the diffusion of electric vehicles in ChinaA multi-stakeholder perspectiverdquo Research in TransportationEconomics vol 66 pp 46ndash58 2017

[5] S Y He Y-H Kuo and D Wu ldquoIncorporating institutionaland spatial factors in the selection of the optimal locations ofpublic electric vehicle charging facilities A case study of BeijingChinardquo Transportation Research Part C Emerging Technologiesvol 67 pp 131ndash148 2016

[6] C Lu H-C Liu J Tao K Rong and Y-C Hsieh ldquoA keystakeholder-based financial subsidy stimulation for Chinese EVindustrialization A system dynamics simulationrdquoTechnologicalForecasting amp Social Change vol 118 pp 1ndash14 2017

[7] S Guo and H Zhao ldquoOptimal site selection of electric vehiclecharging station by using fuzzy TOPSIS based on sustainabilityperspectiverdquoApplied Energy vol 158 pp 390ndash402 2015

[8] YWuM Yang H Zhang K Chen and YWang ldquoOptimal siteselection of electric vehicle charging stations based on a cloudmodel and the PROMETHEE methodrdquo Energies vol 9 no 32016

[9] W Tu Q Li Z Fang S-L Shaw B Zhou and X ChangldquoOptimizing the locations of electric taxi charging stations Aspatialndashtemporal demand coverage approachrdquo TransportationResearch Part C Emerging Technologies vol 65 pp 172ndash1892016

[10] R Riemann D Z W Wang and F Busch ldquoOptimal location ofwireless charging facilities for electric vehicles Flow-capturinglocation model with stochastic user equilibriumrdquo Transporta-tion Research Part C Emerging Technologies vol 58 pp 1ndash122015

[11] S Opricovic and G H Tzeng ldquoCompromise solution byMCDM methods A comparative analysis of VIKOR andTOPSISrdquo European Journal of Operational Research vol 156 no2 pp 445ndash455 2004


[12] S Opricovic and G Tzeng ldquoExtended VIKOR method incomparison with outranking methodsrdquo European Journal ofOperational Research vol 178 no 2 pp 514ndash529 2007

[13] Y Ou Yang H Shieh J Leu and G Tzeng ldquoA VIKOR-basedmultiple criteria decision method for improving informationsecurity riskrdquo International Journal of Information Technologyamp Decision Making vol 08 no 02 pp 267ndash287 2009

[14] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 no 1 pp 87ndash96 1986

[15] R R Yager and A M Abbasov ldquoPythagorean membershipgrades complex numbers and decision makingrdquo InternationalJournal of Intelligent Systems vol 28 no 5 pp 436ndash452 2013

[16] X Peng H Yuan and Y Yang ldquoPythagorean fuzzy informationmeasures and their applicationsrdquo International Journal of Intel-ligent Systems vol 32 no 10 pp 991ndash1029 2017

[17] M Lu G Wei F E Alsaadi T Hayat and A Alsaedi ldquoHesitantpythagorean fuzzy hamacher aggregation operators and theirapplication to multiple attribute decision makingrdquo Journal ofIntelligent amp Fuzzy Systems Applications in Engineering andTechnology vol 33 no 2 pp 1105ndash1117 2017

[18] X Zhang ldquoPythagorean fuzzy clustering analysis A hierar-chical clustering algorithm with the ratio index-based rankingmethodsrdquo International Journal of Intelligent Systems 2017

[19] X L Zhang and Z S Xu ldquoExtension of TOPSIS to multiplecriteria decision making with pythagorean fuzzy setsrdquo Interna-tional Journal of Intelligent Systems vol 29 no 12 pp 1061ndash10782014

[20] X Zhang ldquoA novel approach based on similarity measure forpythagorean fuzzy multiple criteria group decision makingrdquoInternational Journal of Intelligent Systems vol 31 no 6 pp 593ndash611 2016

[21] N Yalcin andU Unlu ldquoAmulti-criteria performance analysis ofinitial public offering (IPO) firms using critic and vikor meth-odsrdquo Technological and Economic Development of Economy vol24 no 2 pp 534ndash560 2018

[22] L Wang H-Y Zhang J-Q Wang and L Li ldquoPicture fuzzynormalized projection-based VIKOR method for the risk eval-uation of construction projectrdquoApplied Soft Computing vol 64pp 216ndash226 2018

[23] M Tavana D Di Caprio and F J Santos-Arteaga ldquoAn extendedstochastic VIKORmodel with decisionmakerrsquos attitude towardsriskrdquo Information Sciences vol 432 pp 301ndash318 2018

[24] B Sennaroglu and G Varlik Celebi ldquoAmilitary airport locationselection by AHP integrated PROMETHEE and VIKOR meth-odsrdquo Transportation Research Part D Transport and Environ-ment vol 59 pp 160ndash173 2018

[25] M Gul B Guven and A F Guneri ldquoA new Fine-Kinney-basedrisk assessment framework using FAHP-FVIKOR incorpora-tionrdquo Journal of Loss Prevention in the Process Industries vol 53pp 3ndash16 2017

[26] P Shojaei S A Seyed Haeri and S Mohammadi ldquoAirportsevaluation and rankingmodel usingTaguchi loss function best-worst method and VIKOR techniquerdquo Journal of Air TransportManagement vol 68 pp 4ndash13 2017

[27] H Gupta ldquoEvaluating service quality of airline industry usinghybrid best worst method andVIKORrdquo Journal of Air TransportManagement vol 68 pp 35ndash47 2018

[28] Y Feng Z Hong G Tian Z Li J Tan and H Hu ldquoEnviron-mentally friendly MCDM of reliability-based product optimi-sation combining DEMATEL-based ANP interval uncertaintyand Vlse Kriterijumska Optimizacija Kompromisno Resenje(VIKOR)rdquo Information Sciences vol 442-443 pp 128ndash144 2018

[29] T Chen ldquoA novel VIKOR method with an application tomultiple criteria decision analysis for hospital-based post-acutecare within a highly complex uncertain environmentrdquo NeuralComputing and Applications 2018

[30] A Awasthi K Govindan and S Gold ldquoMulti-tier sustainableglobal supplier selection using a fuzzy AHP-VIKOR basedapproachrdquo International Journal of Production Economics vol195 pp 106ndash117 2018

[31] A Mardani E K Zavadskas K Govindan A A Seninand A Jusoh ldquoVIKOR technique A systematic review of thestate of the art literature on methodologies and applicationsrdquoSustainability vol 8 no 1 pp 1ndash38 2016

[32] M Gul E Celik N Aydin A Taskin Gumus and A F GunerildquoA state of the art literature review of VIKOR and its fuzzyextensions on applicationsrdquoApplied Soft Computing vol 46 pp60ndash89 2016

[33] W Xue Z Xu X Zhang and X Tian ldquoPythagorean fuzzyLINMAP method based on the entropy theory for railwayproject investment decision makingrdquo International Journal ofIntelligent Systems vol 33 no 1 pp 93ndash125 2018

[34] D Liang Z Xu D Liu and Y Wu ldquoMethod for three-waydecisions using ideal TOPSIS solutions at Pythagorean fuzzyinformationrdquo Information Sciences vol 435 pp 282ndash295 2018

[35] E Ilbahar A Karasan S Cebi and C Kahraman ldquoA novelapproach to risk assessment for occupational health and safetyusing Pythagorean fuzzy AHPamp fuzzy inference systemrdquo SafetyScience vol 103 pp 124ndash136 2018

[36] T-Y Chen ldquoRemoteness index-based Pythagorean fuzzyVIKOR methods with a generalized distance measure formultiple criteria decision analysisrdquo Information Fusion vol 41pp 129ndash150 2018

[37] U B Baloglu and Y Demir ldquoAn agent-based pythagorean fuzzyapproach for demand analysis with incomplete informationrdquoInternational Journal of Intelligent Systems vol 33 no 5 pp983ndash997 2018

[38] X Zhang ldquoMulticriteria Pythagorean fuzzy decision analysisA hierarchicalQUALIFLEX approachwith the closeness index-based rankingmethodsrdquo Information Sciences vol 330 pp 104ndash124 2016

[39] P Ren Z Xu and X Gou ldquoPythagorean fuzzy TODIMapproach to multi-criteria decision makingrdquo Applied Soft Com-puting vol 42 pp 246ndash259 2016

[40] S Zeng Z Mu T Baleentis and T Balezentis ldquoA novelaggregation method for Pythagorean fuzzy multiple attributegroup decision makingrdquo International Journal of IntelligentSystems vol 33 no 3 pp 573ndash585 2018

[41] G Wei and M Lu ldquoPythagorean fuzzy Maclaurin symmetricmean operators in multiple attribute decisionmakingrdquo Interna-tional Journal of Intelligent Systems vol 33 no 5 pp 1043ndash10702018

[42] G Wei and M Lu ldquoPythagorean fuzzy power aggregationoperators in multiple attribute decision makingrdquo InternationalJournal of Intelligent Systems vol 33 no 1 pp 169ndash186 2018

[43] D Liang Y Zhang Z Xu and A P Darko ldquoPythagoreanfuzzy Bonferronimean aggregation operator and its accelerativecalculating algorithm with the multithreadingrdquo InternationalJournal of Intelligent Systems vol 33 no 3 pp 615ndash633 2018

[44] H Garg ldquoSome methods for strategic decision-making prob-lems with immediate probabilities in Pythagorean fuzzy envi-ronmentrdquo International Journal of Intelligent Systems vol 33 no4 pp 687ndash712 2018


[45] W Yang ldquoA user-choice model for locating congested fastcharging stationsrdquo Transportation Research Part E Logistics andTransportation Review vol 110 pp 189ndash213 2018

[46] J He H Yang T Tang and H Huang ldquoAn optimal chargingstation location model with the consideration of electric vehi-clersquos driving rangerdquo Transportation Research Part C EmergingTechnologies vol 86 pp 641ndash654 2018

[47] F Guo J Yang and J Lu ldquoThe battery charging stationlocation problem Impact of usersrsquo range anxiety and distanceconveniencerdquo Transportation Research Part E Logistics andTransportation Review vol 114 pp 1ndash18 2018

[48] H Liu M Yang M Zhou and G Tian ldquoAn integratedmulti-criteria decision making approach to location planningof electric vehicle charging stationsrdquo IEEE Transactions onIntelligent Transportation Systems 2018

[49] Y Wu C Xie C Xu and F Li ldquoA decision framework forelectric vehicle charging station site selection for residentialcommunities under an intuitionistic fuzzy environment A caseof beijingrdquo Energies vol 10 no 9 2017

[50] S Wu and G Wei ldquoPythagorean fuzzy Hamacher aggregationoperators and their application to multiple attribute decisionmakingrdquo International Journal of Knowledge-Based and Intelli-gent Engineering Systems vol 21 no 3 pp 189ndash201 2017

[51] X Peng and Y Yang ldquoSome results for Pythagorean fuzzy setsrdquoInternational Journal of Intelligent Systems vol 30 no 11 pp1133ndash1160 2015

[52] H-C Liu L-X Mao Z-Y Zhang and P Li ldquoInduced aggre-gation operators in the VIKOR method and its application inmaterial selectionrdquoApplied Mathematical Modelling vol 37 no9 pp 6325ndash6338 2013

[53] Z S Xu ldquoAn overview of methods for determining OWAweightsrdquo International Journal of Intelligent Systems vol 20 no8 pp 843ndash865 2005

[54] H Garg ldquoA novel accuracy function under interval-valuedPythagorean fuzzy environment for solving multicriteria deci-sion making problemrdquo Journal of Intelligent amp Fuzzy SystemsApplications in Engineering and Technology vol 31 no 1 pp529ndash540 2016

[55] Z Liu P Liu W Liu and J Pang ldquoPythagorean uncertainlinguistic partitioned Bonferroni mean operators and theirapplication in multi-attribute decision makingrdquo Journal ofIntelligent amp Fuzzy Systems Applications in Engineering andTechnology vol 32 no 3 pp 2779ndash2790 2017

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deal of attention has been given for the determination of theoptimal location for EVCSs [3 7ndash10]

In practical EVCS site selection processes it is generallyhard to find an alternative that satisfies all criteria at thesame time so a good compromise solution is preferred Thisproblem may become more complex when multiple decisionmakers are involved each having a different perception onthe alternatives Therefore the optimal siting of EVCSs hasalways been a problemwhich can be effectively solved bymul-ticriteria decision-making (MCDM) methods The VIKOR(VIsekriterijumska optimizacija i KOmpromisno Resenje)method initially proposed by Opricovic and Tzeng [11] is anefficient tool to solve group decision-making problems withcontradictory and noncommensurable criteria It assumesthat compromising is adequate for conflict resolution thedecision maker wants a solution which is the closest to theideal and the alternatives are ordered based on all predefinedcriteria [12 13] This technique is a helpful tool in thesituations where a decision maker is not able to indicatepreferences among alternatives that may result in varied con-sequences Because of its characteristics and competenciesthe VIKOR method is a promising tool to find the optimallocation of EVCSs

Normally the techniques such as initial interview fieldinvestigation and programming (optimization) models wereused for the optimal location of EVCSs [7] However withthe increasing complexity of EVCS site selection problemsdecisionmakers often need to consider multiple criteria suchas the effect on ecological environment the investment payoffperiod and the attitude of local residents to make decisionsThere are also some situations when the assessments ofalternatives must cope with the vagueness of establishedcriteria and the development of a fuzzy MCDM method isneeded to handle either qualitative or incomplete data [2 78] As a generalization of intuitionistic fuzzy sets [14] thePythagorean fuzzy sets (PFSs) were introduced by Yager andAbbasov [15] The PFSs are also characterized by a member-ship degree and a nonmembership degree whose square sumis less than or equal to 1 but the sum is not required to be lessthan one Consequently the theory of PFSs can depict moreimprecise and ambiguous information in solving MCDMproblems [16ndash18] In many real circumstances particularlyin the process of group decision-making under uncertaintythe judgments or preferences provided by decision makersmay be appropriately expressed in Pythagorean fuzzy values(PFVs) [19] Thus PFSs can be very useful to manage thesubjective evaluations of domain experts in the EVCS siteselection

Based on above discussions this paper presents aPythagorean fuzzy VIKOR (PF-VIKOR) method to selectthe optimal site of EVCSs under Pythagorean fuzzy envi-ronment Specifically the evaluations of alternatives againsteach criterion are treated as linguistic terms which can bedenoted by PFVsThe Pythagorean fuzzy weighted averaging(PFWA) operator [20] emphasizing the individual influenceis employed to aggregate all decision makersrsquo opinions intogroup assessments Particularly the generalized Pythagoreanfuzzy ordered weighted standardized distance (GPFOWSD)operator is proposed to calculate the utility and regret

measures of the PF-VIKOR The new model can not onlyinclude the attitudinal character of a decision maker for thesite selection of EVCSs but also parameterize the results fromthe minimum to the maximum according to the decisionmakerrsquos interests Thus it is able to provide a wide range ofsituations according to the attitude taken by a decision makerin the particular application considered

The rest of this paper is outlined as follows in Section 2a review of the existing literature related to this study isincluded In Section 3 somebasic concepts related to PFSs arereviewed and theGPFOWSDoperator is developed Section 4provides the PF-VIKORmethod to group EVCS site selectionA numerical example is provided in Section 5 to illustrate theproposed approach and a comparative analysis is conductedto display the advantages of the new EVCS site selectionmodel Finally conclusions of this article are presented inSection 6

2 Literature Review

21 Application of VIKOR Method Recently the VIKORmethod has been successfully utilized by scholars to handlevarious decision-making problems For example Yalcın andUnlu [21] used VIKOR and CRiteria Importance ThroughIntercriteria Correlation (CRITIC) methods for the multicri-teria performance evaluation of initial public offering firmsWang et al [22] presented an integrated model based onVIKOR and entropy weight methods for the risk evaluationof construction project under picture fuzzy environmentTavana et al [23] constructed an extended VIKOR approachthat accounts for differences in the risk attitudes of decisionmakers when ranking stochastic alternatives Sennaroglu andVarlik Celebi [24] solved the location selection problem fora military airport by combining analytic hierarchy process(AHP) and VIKOR methods Gul et al [25] proposed amodeling framework incorporating fuzzy AHP with fuzzyVIKOR for occupational health and safety risk assess-ment Shojaei et al [26] proposed an integration methodusing Taguchi loss function best-worst method and VIKORtechnique to evaluate and rank airports and Gupta [27]evaluated the service quality of airline industry using ahybrid approach consisting of best-worstmethod andVIKORmethod In [28] an environmentally friendly decision-making model using decision-making trial and evaluationlaboratory- (DEMATEL-) based analytical network process(ANP) (DANP) interval uncertainty and VIKOR methodwas presented for the reliability-based product optimizationIn [29] a compromising decision-making method based oninterval-valued Pythagorean fuzzy sets and VIKOR methodwas developed and applied to decision analysis for hospital-based post-acute care In [30] the authors employed an inte-grated fuzzy AHP-VIKOR framework for multi-tier sustain-able global supplier selection Besides a systematic review ofthe literature on the VIKOR method and its applications canbe found in [31 32]

22 Application of PFSs The PFSs have received wide atten-tion in recent years and many researchers have applied it toaddress a variety of real-world decision-making problems






3 Preliminaries



119875 = ⟨119909 120583119875 (119909) ]119875 (119909)⟩ | 119909 isin 119883 (1)







119878 (119901) = 12 (1 + (120583119901)2 minus (V119901)2) (2)


119867(119901) = (120583119901)2 + (V119901)2 (3)








(4)



119875119865119882119860(1199011 1199012 119901119899) = 119899⨁119894=1

119908119894119901119894= (radic1 minus 119899prod

119894=1

(1 minus (120583119901119894)2)119908119894 119899prod119894=1

(V119901119894)119908119894) (5)





120596119896119889120582119896)1120582 120582 = 0 (6)





120596119896119889119896 (7)




1205961198961198892119896)12 (8)





119889120596119896119896 (9)










119903119894119895 = PFWA (1199031119894119895 1199032119894119895 119903119897119894119895) = 119897⨁119896=1

120582119896119903119896119894119895


(1 minus (120583119896119894119895)2)119908119896 119897prod119896=1

(V119896119894119895)119908119896) 119894 = 1 2 119898 119895 = 1 2 119899

(10)


= [[[[[[[


]]]]]]] (11)


119901lowast119895 = max119894


min119894


(12)


119901minus119895 = min119894


max119894


(13)


120596119896119889120582119896)1120582 119894 = 1 2 119898 (14)

119877119894 = (max119896

(120596119896119889120582119896))1120582 119894 = 1 2 119898 (15)






























A1 (0817 0184) (0715 0286) (0750 0250) (0729 0272) (0729 0272) (0729 0272)A2 (0802 0199) (0690 0311) (0763 0239) (0850 0150) (0562 0412) (0750 0250)A3 (0715 0286) (0650 0350) (0830 0170) (0826 0175) (0585 0397) (0850 0150)A4 (0850 0150) (0733 0267) (0830 0170) (0781 0220) (0764 0237) (0545 0423)

C7 C8 C9 C10 C11 C12

A1 (0537 0428) (0750 0250) (0720 0281) (0279 0724) (0500 0450) (0652 0343)A2 (0545 0423) (0599 0387) (0469 0493) (0328 0674) (0395 0593) (0500 0450)A3 (0545 0423) (0792 0209) (0824 0178) (0229 0774) (0619 0373) (0744 0255)A4 (0554 0417) (0769 0232) (0500 0450) (0150 0850) (0545 0423) (0695 0306)






(17)








PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986





A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4












6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018













3 Preliminaries



119875 = ⟨119909 120583119875 (119909) ]119875 (119909)⟩ | 119909 isin 119883 (1)







119878 (119901) = 12 (1 + (120583119901)2 minus (V119901)2) (2)


119867(119901) = (120583119901)2 + (V119901)2 (3)








(4)



119875119865119882119860(1199011 1199012 119901119899) = 119899⨁119894=1

119908119894119901119894= (radic1 minus 119899prod

119894=1

(1 minus (120583119901119894)2)119908119894 119899prod119894=1

(V119901119894)119908119894) (5)





120596119896119889120582119896)1120582 120582 = 0 (6)





120596119896119889119896 (7)




1205961198961198892119896)12 (8)





119889120596119896119896 (9)










119903119894119895 = PFWA (1199031119894119895 1199032119894119895 119903119897119894119895) = 119897⨁119896=1

120582119896119903119896119894119895


(1 minus (120583119896119894119895)2)119908119896 119897prod119896=1

(V119896119894119895)119908119896) 119894 = 1 2 119898 119895 = 1 2 119899

(10)


= [[[[[[[


]]]]]]] (11)


119901lowast119895 = max119894


min119894


(12)


119901minus119895 = min119894


max119894


(13)


120596119896119889120582119896)1120582 119894 = 1 2 119898 (14)

119877119894 = (max119896

(120596119896119889120582119896))1120582 119894 = 1 2 119898 (15)






























A1 (0817 0184) (0715 0286) (0750 0250) (0729 0272) (0729 0272) (0729 0272)A2 (0802 0199) (0690 0311) (0763 0239) (0850 0150) (0562 0412) (0750 0250)A3 (0715 0286) (0650 0350) (0830 0170) (0826 0175) (0585 0397) (0850 0150)A4 (0850 0150) (0733 0267) (0830 0170) (0781 0220) (0764 0237) (0545 0423)

C7 C8 C9 C10 C11 C12

A1 (0537 0428) (0750 0250) (0720 0281) (0279 0724) (0500 0450) (0652 0343)A2 (0545 0423) (0599 0387) (0469 0493) (0328 0674) (0395 0593) (0500 0450)A3 (0545 0423) (0792 0209) (0824 0178) (0229 0774) (0619 0373) (0744 0255)A4 (0554 0417) (0769 0232) (0500 0450) (0150 0850) (0545 0423) (0695 0306)






(17)








PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986





A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4












6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018











119878 (119901) = 12 (1 + (120583119901)2 minus (V119901)2) (2)


119867(119901) = (120583119901)2 + (V119901)2 (3)








(4)



119875119865119882119860(1199011 1199012 119901119899) = 119899⨁119894=1

119908119894119901119894= (radic1 minus 119899prod

119894=1

(1 minus (120583119901119894)2)119908119894 119899prod119894=1

(V119901119894)119908119894) (5)





120596119896119889120582119896)1120582 120582 = 0 (6)





120596119896119889119896 (7)




1205961198961198892119896)12 (8)





119889120596119896119896 (9)










119903119894119895 = PFWA (1199031119894119895 1199032119894119895 119903119897119894119895) = 119897⨁119896=1

120582119896119903119896119894119895


(1 minus (120583119896119894119895)2)119908119896 119897prod119896=1

(V119896119894119895)119908119896) 119894 = 1 2 119898 119895 = 1 2 119899

(10)


= [[[[[[[


]]]]]]] (11)


119901lowast119895 = max119894


min119894


(12)


119901minus119895 = min119894


max119894


(13)


120596119896119889120582119896)1120582 119894 = 1 2 119898 (14)

119877119894 = (max119896

(120596119896119889120582119896))1120582 119894 = 1 2 119898 (15)






























A1 (0817 0184) (0715 0286) (0750 0250) (0729 0272) (0729 0272) (0729 0272)A2 (0802 0199) (0690 0311) (0763 0239) (0850 0150) (0562 0412) (0750 0250)A3 (0715 0286) (0650 0350) (0830 0170) (0826 0175) (0585 0397) (0850 0150)A4 (0850 0150) (0733 0267) (0830 0170) (0781 0220) (0764 0237) (0545 0423)

C7 C8 C9 C10 C11 C12

A1 (0537 0428) (0750 0250) (0720 0281) (0279 0724) (0500 0450) (0652 0343)A2 (0545 0423) (0599 0387) (0469 0493) (0328 0674) (0395 0593) (0500 0450)A3 (0545 0423) (0792 0209) (0824 0178) (0229 0774) (0619 0373) (0744 0255)A4 (0554 0417) (0769 0232) (0500 0450) (0150 0850) (0545 0423) (0695 0306)






(17)








PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986





A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4












6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018












119889120596119896119896 (9)










119903119894119895 = PFWA (1199031119894119895 1199032119894119895 119903119897119894119895) = 119897⨁119896=1

120582119896119903119896119894119895


(1 minus (120583119896119894119895)2)119908119896 119897prod119896=1

(V119896119894119895)119908119896) 119894 = 1 2 119898 119895 = 1 2 119899

(10)


= [[[[[[[


]]]]]]] (11)


119901lowast119895 = max119894


min119894


(12)


119901minus119895 = min119894


max119894


(13)


120596119896119889120582119896)1120582 119894 = 1 2 119898 (14)

119877119894 = (max119896

(120596119896119889120582119896))1120582 119894 = 1 2 119898 (15)






























A1 (0817 0184) (0715 0286) (0750 0250) (0729 0272) (0729 0272) (0729 0272)A2 (0802 0199) (0690 0311) (0763 0239) (0850 0150) (0562 0412) (0750 0250)A3 (0715 0286) (0650 0350) (0830 0170) (0826 0175) (0585 0397) (0850 0150)A4 (0850 0150) (0733 0267) (0830 0170) (0781 0220) (0764 0237) (0545 0423)

C7 C8 C9 C10 C11 C12

A1 (0537 0428) (0750 0250) (0720 0281) (0279 0724) (0500 0450) (0652 0343)A2 (0545 0423) (0599 0387) (0469 0493) (0328 0674) (0395 0593) (0500 0450)A3 (0545 0423) (0792 0209) (0824 0178) (0229 0774) (0619 0373) (0744 0255)A4 (0554 0417) (0769 0232) (0500 0450) (0150 0850) (0545 0423) (0695 0306)






(17)








PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986





A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4












6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018









119901minus119895 = min119894


max119894


(13)


120596119896119889120582119896)1120582 119894 = 1 2 119898 (14)

119877119894 = (max119896

(120596119896119889120582119896))1120582 119894 = 1 2 119898 (15)






























A1 (0817 0184) (0715 0286) (0750 0250) (0729 0272) (0729 0272) (0729 0272)A2 (0802 0199) (0690 0311) (0763 0239) (0850 0150) (0562 0412) (0750 0250)A3 (0715 0286) (0650 0350) (0830 0170) (0826 0175) (0585 0397) (0850 0150)A4 (0850 0150) (0733 0267) (0830 0170) (0781 0220) (0764 0237) (0545 0423)

C7 C8 C9 C10 C11 C12

A1 (0537 0428) (0750 0250) (0720 0281) (0279 0724) (0500 0450) (0652 0343)A2 (0545 0423) (0599 0387) (0469 0493) (0328 0674) (0395 0593) (0500 0450)A3 (0545 0423) (0792 0209) (0824 0178) (0229 0774) (0619 0373) (0744 0255)A4 (0554 0417) (0769 0232) (0500 0450) (0150 0850) (0545 0423) (0695 0306)






(17)








PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986





A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4












6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018





















A1 (0817 0184) (0715 0286) (0750 0250) (0729 0272) (0729 0272) (0729 0272)A2 (0802 0199) (0690 0311) (0763 0239) (0850 0150) (0562 0412) (0750 0250)A3 (0715 0286) (0650 0350) (0830 0170) (0826 0175) (0585 0397) (0850 0150)A4 (0850 0150) (0733 0267) (0830 0170) (0781 0220) (0764 0237) (0545 0423)

C7 C8 C9 C10 C11 C12

A1 (0537 0428) (0750 0250) (0720 0281) (0279 0724) (0500 0450) (0652 0343)A2 (0545 0423) (0599 0387) (0469 0493) (0328 0674) (0395 0593) (0500 0450)A3 (0545 0423) (0792 0209) (0824 0178) (0229 0774) (0619 0373) (0744 0255)A4 (0554 0417) (0769 0232) (0500 0450) (0150 0850) (0545 0423) (0695 0306)






(17)








PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986





A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4












6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018











PFNHSD S 0592 0652 0106 0606R 0083 0083 0042 0083Q 0945 1000 0000 0958

PFNESD S 0661 0749 0208 0732R 0289 0289 0145 0289Q 0919 1000 0000 0985

PFWHSD S 0551 0596 0129 0644R 0097 0114 0063 0125Q 0686 0872 0000 1000

PFWESD S 0638 0710 0230 0763R 0311 0338 0178 0353Q 0764 0909 0000 1000

PFOWHSD S 0606 0690 0068 0641R 0092 0114 0025 0116Q 0798 0989 0000 0960

PFOWESD S 0649 0758 0157 0742R 0260 0338 0107 0338Q 0741 1000 0000 0986





A1 0519 1000 0897 2 0523 2 0452 2A2 0539 1000 0914 3 0384 3 0370 3A3 0059 0376 0000 1 0955 1 0929 1A4 0638 1000 1000 4 0345 4 0344 4












6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018














6 Conclusions






Acknowledgments


References

































































Journal of












Journal of







Volume 2018






Volume 2018





























































Journal of












Journal of







Volume 2018






Volume 2018








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