Rational Supplier Selection Based on Two-Phase Deep ...

Research ArticleRational Supplier Selection Based on Two-Phase DeepAnalysis considering Fuzzy QFD and Game Theory

Feng Li 1 Senhao Luo 2 Yi Wang 1 and Chia-Huei Wu 3

1Department of Management Science and Engineering School of Information Beijing Wuzi University Beijing 101149 China2Department of Management Engineering School of Economics amp Management Xidian University Xirsquoan 710071 China3Department of Hotel Management and Culinary Creativity Minghsin University of Science and TechnologyHsinchu 304 Taiwan

Correspondence should be addressed to Chia-Huei Wu chiahuei530gmailcom

Received 4 March 2021 Revised 23 June 2021 Accepted 15 July 2021 Published 26 July 2021

Academic Editor Hsu-Yang Kung

Copyright copy 2021 Feng Li et alis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Viewing from the perspective of a traditional manufacturing enterprise the paper proposes a fuzzy comprehensive evaluationsystem model which selects the most suitable supplier or suppliers to undertake the supply tasks and to achieve the purposes ofreducing procurement costs and improving the supply quality and reliability so as to fully meet customer demands Based ondecision-makersrsquo preferences and suppliersrsquo supply capabilities subjective and objective weight of criteria are both developed forsupplier selection with the corresponding weighting method namely quality function deployment (QFD) and entropy weightSpecially the two-phase fuzzy QFDmethod combined with the trapezoidal fuzzy number (TFN) is creatively applied to realize thecomplicated conversion process Furthermore the game theory is employed to combine the advantages of the subjective andobjective weightingmethod by which the comprehensive weight can be determined A numerical example is given to demonstratethe proposed modeling process rough programming drawing images for comparative analysis and sensitivity analysis studyimage trends and draw conclusions the proposed model effectively alleviates the weight deviation and has higher rationality andextensibility in supplier selection

1 Introduction

Supplier selection is of great significance to themanufacturing Selecting the optimal supplier can effectivelyreduce the procurement costs and improve the quality andreliability of the supply thereby improving the enterprisersquosprofit margin by minimizing the upstream costs of thesupply chain [1] At the same time it canmake contributionsto improve the customersrsquo satisfaction erefore the sub-jective and objective factors that affect the working efficiencyof the supplier should be considered adequately by manu-facturers Multicriteria decision making (MCDM) methodsthat can effectively determine subjective and objectiveweights of evaluation criteria have been applied to variousfields such as several frequently used methods of obtainingweights include analytic network process (ANP) qualityfunction deployment (QFD) best worst method (BWM)grey relational analysis (GRA) and entropy weight

However both subjective and objective weights have theirown limitations In fact the subjective weight only reflectsthe decision-makersrsquo preferences and ignores the actualefficiency of suppliers which is greatly affected by humanfactors On the contrary the objective weight focuses on theobjective supply capabilities of suppliers and ignores factorssuch as the environment of the manufacturing enterpriseand the interest relationship of the upstream of the supplychain which are closely related to the experience of decisionmakers

Game theory plays an important role in weighing thesubjective and objective weight which uses mathematicaltools to study how the two sides with conflict of interestchoose the optimal strategy respectively [2] In other wordsgame theory mainly studies the decision-making subjectsinteracting with each other how to make decisions and howto achieve equilibrium Game theory was first used as astrategic bargain in economics [3] and then it is widely used

HindawiMobile Information SystemsVolume 2021 Article ID 9979017 12 pageshttpsdoiorg10115520219979017

in the management engineering and many other fields [4]Compared with other tools game theory better deals withthe common disequilibrium in reality and more effectivelymakes individual and collective rationality converge underthe condition of incomplete information and imperfectcompetition In addition game theory provides a replicabletemplate for solving complex interactions between contra-dictory subjects in the process of complex modeling whichis conducive to finding the optimal solution for all parties Itworks well when two or more players have a conflict ofinterest Similarly because the subjective weighting methodis affected by human factors while the objective weightingmethod is absolutely objective there is a big difference in theweight coefficient determined by the two methods for thesame evaluation index Game theory seeks the consistency orcompromise of its correlation weight values in fully con-sidering the foundation of the characteristics of the sub-jective and objective weight method so as to minimize thedeviation of the subjective and objective weight In theprocess they can be regarded as the two sides with conflict ofinterest while the comprehensive weight is regarded as thebenefit combination of the game erefore the compre-hensive weight based on Nash equilibrium is obtained andapplied to rational supplier selection In this paper a rationalweightingmodel combining with game theory is proposed toevaluate and select the most suitable suppliers Consideringboth decision-makersrsquo preferences and suppliersrsquo capabil-ities the subjective and objective weight of supplier evalu-ation criteria are developed for supplier selection with QFDand entropy weight Among them a two-phase fuzzy QFDmethod combined with TFN is creatively used to realize thecomplicated conversion processemost critical step gametheory is employed to combine the advantages of thesubjective and objective weight by which the comprehensiveweight can be determined e structure of the proposedmodel is shown in Figure 1

e remainders of the paper are organized as followsSection 2 is literature review Section 3 introduces thepreliminaries involved in the paper e proposed fusionmodel based on two-phase fuzzy QFD entropy weight andgame theory is introduced in Section 4 Section 5 demon-strates a numerical example to illustrate the effectiveness ofthe proposed model Section 6 makes comparative analysisand sensitivity analysis e final research conclusions arepresented in Section 7

2 Literature Review

Supplier selection is of great significance to the core com-petitiveness of manufacturing enterprises [5] Choosingsuitable suppliers is not only beneficial to reduce inventorycosts and transaction costs but also improve the orderfulfillment rate At the same time information technologyand incentive mechanism are implemented to enable en-terprises and suppliers to become a community of interestsand a rapid reaction system is established in order to shortenthe procurement cycle and make an agile response to marketdemand e common methods and related literature ofsupplier multicriteria evaluation are shown in Table 1

ere are many studies on supplier evaluation and se-lection for manufacturing enterprises Dweiri et al putforward the decision support model of supplier selection inAHP and further carried out sensitivity analysis to test therobustness of supplier selection decision [6] Starting fromthe concept of elasticity Ahmadi et al used AHP to calculatethe weight of sustainable development criteria and inter-feron gamma release assay to rank suppliers and proposed astructured and integrated evaluation decision model forsustainable suppliers in telecommunications industry [7]Zavadskas et al used fuzzy AHP to evaluate and select rawmaterial suppliers for pipeline production [8] Ayag andSamanlioglu comprehensively considered the influence ofquantitative and qualitative factors on supplier selection andproposed an intelligent solution method for the supplierselection problem based on fuzzy ANP [9] Yazdani et alsolved the relationship between customer demands withdecision-making trial and evaluation laboratory (DEMA-TEL) and then determined the degree of relationship be-tween each pair of supplier criteria and customer demandsby the QFD [10] Lima-Junior et al used fuzzy QFD toweight each indicator and then evaluated the degree ofdifficulty of supply to obtain information for each indicatorevaluation [11] Karsak and Dursun proposed a fuzzymulticriteria group decision-making method for supplierselection based on QFD fuzzy information fusion andbinary language representationmodel [12] Gupta and Baruaused BWM to rank selection criteria and then used fuzzyTOPSIS to rank the weight of supplier selection criteriaaiming to select suppliers based on the green innovationability of small- and medium-sized enterprises [13] Rezaeiet al combined with screening and BWM and developed athree-phase supplier selection method [14] Pitchipoo et aladopted grey relational analysis (GRA) as performanceindicators to determine the optimal suppliers then used theprincipal component analysis and entropy weight method toevaluate the corresponding weight values of each perfor-mance indicators and proposed an optional decision-making model to evaluate the relative performance ofsuppliers with multiple outputs and inputs [15] Badi andPamucar applied the mixed grey theory and Marcos methodin a steel companyrsquos supplier selection decision to help itimprove competitiveness [16] Govindan and Sivakumarused the fuzzy technology of similarity ranking with fuzzyTOPSIS to evaluate and select potential suppliers andproposed a model to support the selection of the best greensuppliers and the order allocation among potential suppliers[17] Mousakhani et al took into account the opinions ofpriority experts on the relative importance of criteria cal-culated the weight of decision makers with the extendedinterval-2 fuzzy TOPSIS method sorted the potential al-ternatives according to the interval-2 fuzzy hamming dis-tance measure and proposed a green supplier selectionmodel based on the group decision method [18] Blagojevicet al established a comprehensive entropy fuzzy pivotpairwise relative criteria importance assessment-data en-velopment analysis (PIPRECIA-DEA) model to study howto determine the security state of BampH under particularuncertainty conditions [19] Wei et al obtained the optimal

2 Mobile Information Systems

choice with the largest Euclidean and Hamming distancefrom NIS and designed a probabilistic uncertain languagecoding method based on sine entropy weight which is

applied in green supplier selection [20] In order to obtainthe optimal green supplier Wei et al provided an integratedmodel of entropy weight and multiattributive border

Table 1 e common methods and related literature

AHPANP QFD BWM GRA TOPSIS Entropy weight Game theoryZavadskas et al Dweiri et al Ahmadi et al Ayag et al Yazdani et al Lima-Junior et al Karsak et al Gupta et al Rezaei et al Pitchipoo et al Badi and Pamucar Govindan et al Mousakhani et al Blagojevic et al Wei et al Wei et al Lai et al Liu et al

Supply capability analysis of suppliers

Determine importance levels ofcustomer demands

Obtain manufacture criteria weightsby phase 1

Obtain supplier criteria weightsby phase 2

Defuzzy and obtain subjective weights

Evaluation criteria architecture

Obtain raw data matrix

Normalize raw data matrix

Define entropy

Entro

py w

eigh

t

Two-

phas

e fuz

zy Q

FD m

etho

d

Gam

e the

oryDetermine weight coefficientsAssume weight coefficientsNormalize weights

Score and rank suppliers Normalize weight coefficients Obtain comprehensive weights

Calculate entropy weight and obtainobjective weights

Figure 1 e structure of the proposed model

Mobile Information Systems 3

approximation area comparison (MABAC) under uncertainprobabilistic linguistic sets (UPLTSs) Information entropyis used to calculate the weight of criteria and UPLTSs areused to get the final ranking results of green suppliers [21]At the same time there are many innovative methods forsupplier evaluation and selection Hosseini and Khaleddiscussed the elasticity criteria of supplier selection com-bined binomial logistic regression classification regressiontree and neural network used the integrated method topredict the elasticity of a single supplier and used differentsupplier selection models to rank [22] Chakraborty et alapplied D-number to solve the uncertainty problem in theprocess of supplier selection [23] Durmic used the fullconsistency method (FUCOM) to determine the importanceof the criteria [24] Xiao et al used criteria importancethrough the intercriteria correlation (CRITIC) method todetermine the weight of criteria and proposed a newintuitionistic fuzzy multicriteria group decision-makingmethod Finally an application example of green supplierselection in iron and steel industry is given and an objectiveweighting method is used to improve the effectiveness ofevaluation [25] Lei et al proposed probabilistic uncertainlinguistic QUALIFLEX (PUL-QUALIFLEX) with theCRITIC method to obtain the optimal solution and appliedthe method to an application example of green supplierselection [26] In the research on the flood risk assessmentmodel based on fuzzy comprehensive evaluation Lai et alused AHP and entropy weight method to calculate thesubjective and the objective weight respectively andcombined the two with game theory to reflect the intentionof decision makers and the information content provided byeach indicator effectively correcting the one side of thesingle weight method [27] en in order to overcome thedeficiency that AHP cannot deal with the dependence andinteraction between elements at different levels quantita-tively Liu et al proposed an ANP method based on gametheory which effectively solved the problem of supplierselection under uncertain environment and adjusted theindex weight with DEMATEL making the evaluation resultmore reasonable [1]

However the previous studies still have some draw-backs or challenges QFD has the advantage of fully payingattention to customer demands so many studies applyQFD to supplier selection However most of them thatinvolve the QFD method only implement once or ignorethe manufacturer criteria and directly implement theconversion from customer demands to supplier criteriawhich makes the conversion process between criteria havegap and the connection is not tight enough Entropyweight has absolute objectivity More importantly bothsubjective and objective weights have limitations In orderto overcome these drawbacks a fuzzy two-phase QFDmethod combined with TFN is creatively used to realize thecomplicated conversion process to select the most suitablesupplier or suppliers to fully meet customer demands Onthe basis of fully considering the characteristics of fuzzyQFD and entropy weight methods the paper applies gametheory to seek for the consistency or compromise ofsubjective and objective weight values from the perspective

of a traditional manufacturing enterprise so as to minimizethe deviation of subjective and objective weights

3 Materials and Methods

31 Quality Function Deployment QFD also known ashouse of quality (HOQ) is a customer-driven product de-velopment method Starting from the perspective of qualityassurance customer demands can be obtained throughcertain market survey methods converting customer de-mands into technical demands in the product developmentstage by the matrix graphic method and identifying whichparameter is the most important to customer satisfactionese key parameters form the measurement index of designcontent and are finally decomposed into various stages andfunctional departments of product development In order toensure the quality of final products it is necessary to co-ordinate the work of various departments to make theproducts designed and manufactured truly meet the re-quirements of customers

HOQ is the core tool for establishing the quality functiondeployment system It realizes the quality function de-ployment process through a series of charts and matrices[28] As shown in Figure 2(a) the HOQ looks like a housewith a row and columnmatrix filled with quantized values atthe center of the house e left wall represents the customerattributes namely customer demands (WHATs) while theceiling is usually defined as product requirements (HOWs)ie how to design products to meet customer demands equantitative relationship between WHATs and HOWs is thecore element of the QFD process Other parts of the HOQstructure provide supporting information for the QFD Tobe specific the HOQ consists of the following parts (A)represents the needs of customers (B) represents engi-neering characteristics or methods (C) represents the re-lationship matrix between WHATs and HOWs (D)indicates the level of importance of expectations (E) rep-resents the customer benchmark (F) represents the rela-tionship among engineering characteristics

QFD originated from the Japanese industry and graduallybecame a standard planning tool integrating collectionanalysis and optimization after the promotion by theAmericans [29] e main functions of QFD are reducingdesign changes shorten development cycle improve qualityimprove customer satisfaction and reduce design andmanufacturing costs QFD is applicable to both new productdevelopment and old product improvement suitable for bothgeneral products and large complex products It applies toboth hardware and software products and service manage-ment and it is an indispensable tool in the six sigma designprocess [30] Toyota General Motors Volkswagen Ford andChrysler all use QFD technology in the product planningprocess For example Toyota reduces the production cost of acommercial vehicle by 61 through QFD technology

32 Entropy Weight Information entropy theory wasoriginally introduced by Shannon from thermodynamics toinformation theory [31] and has been widely applied in


decision science social economy and other fields Infor-mation entropy is an uncertain measure of a system in adisordered state [32] and for the entropy weight it canreflect the useful quantitative information of the evaluationindexes Supposing that there are m different states in asystem and the probability of each state is Pi (i 1 2 m)then the entropy of the system is

E minus1

ln m1113944

m

i1pi ln pi (1)

e basic idea of the entropy weight method is todetermine the objective weight according to the indexvariability [33] Generally speaking the smaller the in-formation entropy E of an index is the greater the variationdegree of the index value is the more information it canprovide the greater the role it can play in the compre-hensive evaluation and the greater its weight will be [19]On the contrary the higher the information entropy E of anindex is the smaller the variation degree of the index is theless the information it provides the smaller the role it playsin the comprehensive evaluation and the smaller its weightis [34] Entropy weighting steps are shown in detail inSection 42

33 Game 4eory e study of game theory originated inthe 18th century and developed in the work of ZermeloBorel and Von Neumann [35] In 1944 Von Neumann andMorgenstern published 4e 4eory of Games and EconomicBehavior [36] which laid a solid foundation for the theoriesand methods of cooperative games In 1951 Nash proposedthe concept of Nash equilibrium [37 38] from which gametheory began to flourish and was applied in economicspsychology politics and other fields

Noncooperative static game with complete informationalso known as a strategic game is mainly composed of threeelements participants strategy set and utility function Ingame theory players are both rational and selfish Eachplayer has a set of all possible choices of strategies and thespecific combination of strategies of all players correspondsto a utility function e utility function is an indicator tomeasure the benefit of participants from the game It notonly depends on the strategy choice of participants them-selves but also is related to the strategies of other partici-pants reflecting the preferences of participants for the set ofstrategies In the process of the game when considering theopponentrsquos strategy choice no participant has the motiva-tion to deviate from the strategy he chose and the Nashequilibrium is reached Nash equilibrium is the best

F (x)

1

0 a1 a2 a3 a4 x

(F)The relationship

among engineeringcharacteristics

Manufacturertechniques

Suppliercapacities

Interrelation matrix Ibetween criteria

Interrelation matrix IIbetween criteria

Phase 1

Phase 2

Custo

mer

dem

ands

Man

ufac

ture

rte

chni

ques

(B)Engineering characteristics

or methods

(E)The customer

benchmark

(A)The needs of

customers

(C)The relationship matrix

between WHATs and HOWs

(D)The level of importance of

expectations

(a)

(b) (c)

Figure 2 e graphics involved in preliminaries


response of each participant to a given strategy from anotherparticipant

34 TFN Compared with traditional mathematics and realnumbers the fuzzy number is an important concept in fuzzyanalysis In 1976 Zadeh introduced the concept of fuzzynumbers Since then many scholars have carried out re-search on fuzzy numbers and proposed several fuzzynumbers of different backgrounds [39] such as L-R fuzzynumber triangular fuzzy number and TFN Now the studyof the fuzzy number has become more and more maturesince TFN is an extension of the triangular fuzzy numberand interval fuzzy number which has a wider range ofapplications

In previous literature most scholars used TFN to dealwith problems However since TFN is represented by fourparameters which provide more detailed description it canprovide more detailed solutions than triangular fuzzynumbers As shown in Figure 2(b) TFN can be defined byfour parameters (a1 a2 a3 and a4) and the expression forthe piecewise function [40] is as follows

F(x)

x minus a1

a2 minus a1 if x isin a1 a21113858 1113857

1 if x isin a2 a31113858 1113857

a4 minus x


0 otherwise

where a1 le a2 le a3 le a4

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)

4 The Two-Phase Deep Analysis consideringFuzzy QFD and Game Theory

41 Applying Two-Phase Fuzzy QFD to Calculate SubjectiveWeight By using the two-phase fuzzy QFD method thecomplicated conversion process of customer demands tomanufacturer techniques and to supplier capabilities is re-alized and then the subjective weight is calculated econversion process between criteria is shown in Figure 2 Inaddition in order to make the evaluation more practical theQFD relational matrix uses TFN to provide more detaileddescription

According to the previous research assuming that agroup of TFN evaluation scale is represented byΩ ELMLMMHEH the specific meaning is shown inFigure 3

After completing the evaluation with TFN and calcu-lating the subjective weight of supplier evaluation criteriabased on the evaluation results equations (3) and (4) areused to defuzzify and normalize the evaluation

Qi 14

1113944

4

a1fa i 1 2 m a 1 2 3 and 4 (3)

NQi Qi minus Mini12mQi

Maxi12mQi minus Mini12mQi

(4)

where fa is the fuzzy evaluation value of the trapezoid vertexa 1 2 3 and 4 Qi defines the defuzzified weight of the ithsupplier evaluation criterion NQi is its normalized weighti 1 2 m and m is the number of supplier evaluationcriteria

42 Using Entropy Weight to Calculate Objective Weight

Step 1 normalizing the raw data matrix there are mevaluation criteria and n evaluation objects and theoriginal data matrix B is as follows

B

b11 b1n

⋮ ⋱ ⋮

bm1 middot middot middot bmn

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (5)

After normalizing the matrix C (cij)mtimesn is obtainedwhere the content of symbol cij is the normalized valueof the jth evaluation object on the ith evaluation cri-terion j 1 2 n e normalization formulas ofpositive and negative indicators are respectively asfollows

cij bij minus Minj12nbij

Maxj12nbij minus Minj12nbij

(6)

cij Maxj12nbij minus bij


(7)

Step 2 defining entropy based on the original datamatrix in Step 1 the entropy of the ith evaluationcriterion is defined as the following equation

Ei minush 1113944n

j1dij ln dij i 1 2 m (8)

where

h 1

ln n

dij cij

1113936nj1cij

(9)

Step 3 calculating entropy weight based on the entropyobtained in Step 2 the entropy weight of the ithevaluation criterion is obtained through the followingformulas


WEi 1 minus Ei

m minus 1113936mi1Ei

(10)

where

1113944

m

i1WEi 1 0leWEi le 1 (11)

43 Comprehensive Weight Based on Game 4eory

Step 1 unifying vector definitions use the followingequation to unify the definition of each weight vector

vt ut

ut s1 s2 sm( 1113857

1113944

m

i1si 1

(12)

where ut represents the weight vector obtained bySection 42 t 1 2 r rgt 1 and m is the number ofsupplier evaluation criteriaStep 2 assuming weight coefficients assume that theweight coefficient of each kind of weight is ct and thecomprehensive weight Z is expressed as follows

Z 1113944t1

ctvTt ct gt 0 (13)

Step 3 determining weight coefficients the principle ofdetermining ct is to minimize the deviation betweenthe comprehensive weight and each weight

Min Z minus ut

2

1113944t1

ctvTt minus u

Tt

2

(14)

According to the differential properties of the matrix[1] the condition for the optimal first derivative ofequation (14) is as follows

1113944t1

ct times ut times vTt ut times u

Tt (15)

equivalent to

u1 middot vT1 u1 middot v

T2


T2

⋮ ⋮ ⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

c1

c2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u2 middot uT2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(16)

By the above formula the weight coefficients(c1 c2 ) can be solvedStep 4 normalizing weight coefficients weight coeffi-cients are normalized by the following equation

clowastt

ct

1113936t1ct

(17)

So the optimal weight coefficients clowastt are obtainedMeanwhile the optimal comprehensive weight Zlowast isobtained through the following equation

Zlowast

1113944t1

clowastt v

Tt (18)

Step 5 scoring and ranking according to the finalscores and ranking one or more suppliers participatingin the evaluation with the highest score are selected

5 Numerical Experiment

Considering the subjective preferences of decision makersand the objective supply capacities of suppliers the proposedmodel has high extensibility which is generally applicable todifferent criteria for manufacturers or suppliers ereforeassuming that there are suppliers A B C D E F and Gwhose supply capacities are shown in Table 2 the supplycapacities of suppliers are on time delivery rate (SC1) de-fective rate of raw materials (SC2) fast response time (SC3)resistance to interruption risk rate (SC4) and recycling rate(SC5)

51 Evaluation Criteria Architecture Different literaturehave different considerations and interpretations on thesetting of customer and manufacturer evaluation criteriaAfter consulting and contrasting we set the followingevaluation criteria Customer demand criteria are price(CD1) quality (CD2) service (CD3) uniqueness (CD4)

EL

0 1 2 3 4 5 6 7 8 9

EH EL (0 0 1 2) Extreme low

Medium

Medium low

Medium high

Extreme high

ML (1 2 3 4)

M (3 4 5 6)

MH (5 6 7 8)

EH (7 8 9 9)

ML MHM

Figure 3 TFN evaluation scale


and brand (CD5) For the manufacturer technique criteriaprocess optimization (MT1) is an operation method that issuperior to existing processes in order to improve oper-ational efficiency reduce the production cost strictlycontrol the process procedures and reorganize or improvethe original process e low defective rate (MT2) is animportant index to measure the technological level and thebasic guarantee of product quality Flexibility in pro-duction (MT3) is a new requirement put forward bymanufacturing enterprises in the face of rapidly changingmarket demand Customer organization (MT4) refers tothe ability of manufacturing enterprises to attract cus-tomers and maintain customer loyalty Buffer stock (MT5)refers to the inventory quantity higher than the averagedemand which can avoid the expected demand rise orimbalance between production stages It can effectivelyreduce the risk of production interruption resulting in thefailure of raw materials to be delivered on time in a shortperiod of time due to extreme circumstances Enterprisereputation (MT6) can help enterprises establish a goodpublic image and then improve the market competitive-ness of enterprises

52 4e Application of Two-Phase Fuzzy QFD Based on theevaluation scale in Figure 3 the decision makers evaluatecustomer demands and provide importance levels for themas shown in Table 3 e weight values are expressed in awll 1 2 L

In order to reflect the effect of manufacturer techniqueson customer demands the linguistic approach is used againto establish an interrelation matrix e result of which themanufacturer technique is contributing more to customerdemand is easily observed in Table 4

e weight calculation of manufacturer techniques isprocessed and TFN bwm is used to express the result asshown in Table 5

cwn 1

Motimes bw1 otimes c1n( 1113857oplus bw2 otimes c2n( 1113857oplus middot middot middotoplus bwM otimes cMn( 11138571113858 1113859

(19)

where the array of row l and column m of the matrix isindicated by blm m 1 2 M

So far the first phase of the proposed two-phase fuzzy QFDmethod is completed en the matrix reflecting the effect ofsupplier capacities on manufacturer techniques is built at thebeginning of the second phase and shown in Table 6

e weight calculation of supplier capacities is pro-cessed and the result is represented by TFN cwn as shown inTable 7

cwn 1


(20)

where cmn is the array of row m and column n of the matrixn 1 2 N

e fuzzy weight is defuzzified by equation (3) and theresult is shown in Table 8

53 4e Application of Entropy Weight On the basis ofTable 2 the original data can be constructed with matrix B asfollows

B

0953 0945 0872 0846 0935 0862 0820

0012 0014 0010 0013 0013 0010 0015

1500 1850 1300 1800 1750 1200 2200

0693 0610 0782 0759 0620 0792 0735

0550 0612 0657 0604 0622 0667 0550

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)

e matrix A is normalized by equations (6) and (7) toget matrix C

C

1000 0940 0391 0195 0865 0316 0

0600 0200 1000 0400 0400 1000 0

0700 0350 0900 0400 0450 1000 0

0456 0 0945 0819 0055 1000 0687

0 0530 0915 0462 0615 1000 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(22)

ematrix C is processed by equations (8) and (9) to getentropy E1ndashE5

E1 0844 E2 0853 E3 0880 E4 0836 andE5 0804

Table 3 Importance levels of customer demands

Demand Importance level awl

CD1 EH (7899)CD2 EH (7899)CD3 EH (7899)CD4 MH (5678)CD5 MH (5678)

Table 4 Interrelation between customer demands and manufac-turer techniques

CDMT MT1 MT2 MT3 MT4 MT5 MT6

CD1 EH MH EH EH EH MHCD2 EH EH EL EH EL EHCD3 EL EL EH EH EH EHCD4 ML EL ML MH EL EHCD5 ML EH ML MH MH EH

Table 2 e supply capacities of suppliers

Supplier SC1 SC2 SC3 SC4 SC5

A 953 120 150 693 550B 945 140 185 610 612C 872 100 130 782 657D 846 130 180 759 604E 935 130 175 620 622F 862 100 120 792 667G 820 150 220 735 550


Table 5 e weight calculation of manufacturer techniques

CDMT MT1 MT2 MT3 MT4 MT5 MT6 awl

CD1 (7899) (5678) (7899) (7899) (7899) (5678) (7899)CD2 (7899) (7899) (0012) (7899) (0012) (7899) (7899)CD3 (0012) (0012) (7899) (7899) (7899) (7899) (7899)CD4 (1234) (0012) (1234) (5678) (0012) (7899) (5678)CD5 (1234) (7899) (1234) (5678) (5678) (7899) (5678)bwm bw1 bw2 bw3 bw4 bw5 bw6

(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)

Table 6 Interrelation between manufacturer techniques and supplier capacities

MTSC SC1 SC2 SC3 SC4 SC5

MT1 EL EH ML EL ELMT2 EL EH EL ML ELMT3 EH EL MH EH ELMT4 M MH M MH EHMT5 EH EL MH EH ELMT6 MH MH EH MH EH

Table 7 e weight calculation of supplier capacities

MTSC SC1 SC2 SC3 SC4 SC5 bwm

MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)

Table 8 Defuzzification and normalization

Supplier criteria Defuzzification weight Normalization weightSC1 231575 0197SC2 250300 0213SC3 238892 0203SC4 262817 0224SC5 191225 0163Until now the weight calculation of the proposed two-phase fuzzy QFD method is completed


After the entropy E1ndashE5 are obtained and the entropyweight is calculated by equations (10) and (11) as follows

WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250

Until now the weight calculation of entropy weight iscompleted

544eCombinationwith Game4eory Each weight vectorprocessed by equation (12) and unification results are asfollows

v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)

e matrix equation is calculated by equations (13)ndash(16)as follows

With the MATLAB R2019a to assist the calculation theweight coefficientsrsquo vector α can be obtained

c c1 c21113858 1113859 [0398 0615] (23)

Equation (17) is applied to normalize the weight coef-ficients vector α and the optimal comprehensive weightWlowastis obtained by equation (18) as follows

clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)

55 Suppliers Evaluation and Ranking On the basis of theoriginal data matrix B and the optimal comprehensiveweight Zlowast the final scores and ranking of suppliers par-ticipating in the evaluation are calculated as shown inTable 9

erefore the comprehensive ranking of the suppliers isGgtDgtBgtEgtAgtCgt F

6 Comparative Analysis andSensitivity Analysis

In this chapter through comparative analysis and sensitivityanalysis the rationality of the proposed method and theranking result of the suppliers are respectively processed toprove the robustness

61 Comparative Analysis In this section subjective andobjective weights are calculated by fuzzy QFD and entropyweights respectively ese two types of weights and thecomprehensive weight calculated by the proposed methodare drawn in the same coordinate system and the brokenline diagram is shown in Figure 4

From the analysis of the figure it can be seen that theweight value obtained by the single weight method is notconvincing because there is no reference Although sub-jective and objective methods have their own applicabilitythe weight values obtained by different methods vary greatlye proposed method combined with game theory fullyrefers the existing weight values and solves each weight

proportion problem through the combination of weightcoefficients which effectively alleviates the weight deviationUnder the same criterion the comprehensive weight value isalways in the range of subjective and objective weight valueserefore the comprehensive weight is the optimal equi-librium of subjective and objective weights and the pro-posed method combined with game theory is more rationalthan the single method

62 Sensitivity Analysis is section studies the score andranking of suppliers A B C D E F and G when thenormalized subjective weight coefficient clowast1 varies contin-uously in the interval (0 1) and are drawn in Figure 5

Analysis of the figure shows that with the increase of thesubjective weight coefficient the scores of all suppliers areincreasing Suppliers A and G are more sensitive to thesubjective weight coefficient and their scores grow fasterWhen there are no decision makers participating in theevaluation the suppliersrsquo scores are completely determined

Table 9 Score and rank

Supplier Score RankA 0718 5B 0773 3C 0709 6D 0775 2E 0758 4F 0694 7G 0822 1

026

024

022

02

018

016

1 2 3 4 5

5 supplier capacity criteria

Wei

ght v

alue

Fuzzy QFDEntropy weightProposed method

Figure 4 Supplier capacity criteria weights under three methods

0 01

088086084082

08078076074072

07068

02 03 04 05 06 07 08Normalized subjective weight coefficient

Scor

e

09 1

Score AScore BScore CScore D

Score EScore FScore G

Figure 5 e supplier ranking with the variation of the subjectiveweight coefficient


by their own supply capacities When the decision makersparticipate in the evaluation moderately the gap betweensuppliers A and C becomes significant In other words as theparticipation of decision makers increases the gap amongsuppliers will become more obvious e effective partici-pation of decision makers can make it easier to select themost suitable suppliers

7 Conclusions

Supplier selection is of great significance to the core com-petitiveness of manufacturing enterprises e paper pro-poses a fuzzy comprehensive supplier evaluation systemmodel to improve the supply quality and reliability so as tofully meet customer demands Based on decision makersrsquopreferences and suppliersrsquo supply capabilities subjective andobjective weights of criteria are both developed for supplierselection Specially the two-phase fuzzy QFD method iscreatively applied to realize the complicated conversionprocess Furthermore the game theory is employed tocombine the advantages of the subjective and objectiveweighting method by which the comprehensive weight canbe determined Although the objective evaluation methodcan alleviate the excessive subjectivity of decision-making toa certain extent the subjective decision-making ability ofdecision makers can still affect the decision-making processGreen supplier selection computer aided evaluation andartificial intelligence simulation decision are the future re-search direction [41ndash43] rough comparative analysis andsensitivity analysis some revelations are obtained

(1) e proposed method combined with game theoryfully refers the existing weight values and solves eachweight proportion problem through the combina-tion of weight coefficients which effectively alleviatesthe weight deviation erefore the proposedmethod is more rational than the single method

(2) e proposed model has high extensibility in whichthe subjective and objective weight can be replacedby other methods which are more suitable for solvingthe practical problem

(3) When the participation of decision makers increasesthe gap among suppliers will become more obviouse effective participation of decision makers canmake it easier to select the most suitable suppliers

In addition the limitations of the proposed method arethat the subjective evaluation and analysis process of sup-pliers requires decision makers to have sufficient experienceand decision-making ability Computer-aided decision-making can be used as a new combination direction

Data Availability

No data were used to support the findings of this study

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is research was funded by Key Realm RampD Program ofGuangdong Province (2019B020214002) Beijing SocialScience Foundation (19ZDA12 18GLB022 17GLC066 and19GLC051) Beijing Intelligent Logistics System Collabo-rative Innovation Center (BILSCIC-2019KF-12) Beijing KeyLaboratory (no BZ0211) Social Science Program of BeijingMunicipal Education Commission (SM201810037001 andSM201910037004) Beijing Wuzi University Major ResearchProjects (2019XJZD12) ldquoCentral University Science Re-search Foundation of Chinardquo (JB170609) and China Post-doctoral Science Foundation (2016M590929)

References

[1] T Liu Y Deng and F Chan ldquoEvidential supplier selectionbased on DEMATEL and game theoryrdquo International Journalof Fuzzy Systems vol 20 no 4 pp 1321ndash1333 2017

[2] L Sun Y Liu B Zhang Y Shang H Yuan and Z Ma ldquoAnintegrated decision-making model for transformer conditionassessment using game theory and modified evidence com-bination extended by D numbersrdquo Energies vol 9 no 9p 697 2016

[3] A G Sanfey ldquoSocial decision-making insights from gametheory and neurosciencerdquo Science vol 318 no 5850pp 598ndash602 2007

[4] D M Frank and S Sarkar ldquoGroup decisions in biodiversityconservation implications from game theoryrdquo PLoS Onevol 5 no 5 Article ID e10688 2010

[5] G-J Cheng L-T Liu X-J Qiang and Y Liu ldquoIndustry 40development and application of intelligent manufacturingrdquo inProceedings of the 2016 International Conference on Infor-mation System and Artificial Intelligence (ISAI) pp 407ndash410Hong Kong China June 2016

[6] F Dweiri S Kumar S A Khan and V Jain ldquoDesigning anintegrated AHP based decision support system for supplierselection in automotive industryrdquo Expert Systems with Ap-plications vol 62 pp 273ndash283 2016

[7] H B Ahmadi S H Hashemi Petrudi and X Wang ldquoInte-grating sustainability into supplier selection with analyticalhierarchy process and improved grey relational analysis acase of telecom industryrdquo 4e International Journal of Ad-vanced Manufacturing Technology vol 90 no 9ndash12pp 2413ndash2427 2017

[8] E K Zavadskas Z Turskis Z Stevic and A MardanildquoModelling procedure for the selection of steel pipes supplierby applying fuzzy AHP methodrdquo Operational Research inEngineering Sciences 4eory and Applications vol 3 no 2pp 39ndash53 2020

[9] Z Ayag and F Samanlioglu ldquoAn intelligent approach tosupplier evaluation in automotive sectorrdquo Journal of Intelli-gent Manufacturing vol 27 no 4 pp 889ndash903 2014

[10] M Yazdani P Chatterjee E K Zavadskas andS Hashemkhani Zolfani ldquoIntegrated QFD-MCDM frame-work for green supplier selectionrdquo Journal of Cleaner Pro-duction vol 142 pp 3728ndash3740 2017

[11] F R Lima-Junior and L C R Carpinetti ldquoA multicriteriaapproach based on fuzzy QFD for choosing criteria forsupplier selectionrdquo Computers amp Industrial Engineeringvol 101 pp 269ndash285 2016


[12] E E Karsak and M Dursun ldquoAn integrated fuzzy MCDMapproach for supplier evaluation and selectionrdquo Computers ampIndustrial Engineering vol 82 pp 82ndash93 2015

[13] H Gupta and M K Barua ldquoSupplier selection among SMEson the basis of their green innovation ability using BWM andfuzzy TOPSISrdquo Journal of Cleaner Production vol 152pp 242ndash258 2017

[14] J Rezaei T Nispeling J Sarkis and L Tavasszy ldquoA supplierselection life cycle approach integrating traditional and en-vironmental criteria using the best worst methodrdquo Journal ofCleaner Production vol 135 pp 577ndash588 2016

[15] P Pitchipoo P Venkumar and S Rajakarunakaran ldquoGreydecision model for supplier evaluation and selection inprocess industry a comparative perspectiverdquo 4e Interna-tional Journal of Advanced Manufacturing Technology vol 76no 9ndash12 pp 2059ndash2069 2015

[16] I Badi and D Pamucar ldquoSupplier selection for steelmakingcompany by using combined Grey-MARCOS methodsrdquoDecision Making Applications in Management and Engi-neering vol 3 no 2 pp 37ndash48 2020

[17] K Govindan and R Sivakumar ldquoGreen supplier selection andorder allocation in a low-carbon paper industry integratedmulti-criteria heterogeneous decision-making and multi-objective linear programming approachesrdquo Annals of Oper-ations Research vol 238 no 1-2 pp 243ndash276 2015

[18] S Mousakhani S Nazari-Shirkouhi and A Bozorgi-AmirildquoA novel interval type-2 fuzzy evaluation model based groupdecision analysis for green supplier selection problems a casestudy of battery industryrdquo Journal of Cleaner Productionvol 168 pp 205ndash218 2017

[19] A Blagojevic Z Stevic D Marinkovic S Kasalica andS Rajilic ldquoA novel entropy-fuzzy PIPRECIA-DEA model forsafety evaluation of railway trafficrdquo Symmetry vol 12 no 9p 1479 2020

[20] C Wei J Wu Y Guo and G Wei ldquoGreen supplier selectionbased on CODAS method in probabilistic uncertain linguisticenvironmentrdquo Technological and Economic Development ofEconomy vol 27 no 3 pp 530ndash549 2021

[21] G Wei Y He F Lei J Wu C Wei and Y Guo ldquoGreensupplier selection with an uncertain probabilistic linguisticMABAC methodrdquo Journal of Intelligent amp Fuzzy Systemsvol 39 no 3 pp 3125ndash3136 2020

[22] S Hosseini and A A Khaled ldquoA hybrid ensemble and AHPapproach for resilient supplier selectionrdquo Journal of IntelligentManufacturing vol 30 no 1 pp 207ndash228 2016

[23] S Chakraborty R Chattopadhyay and S Chakraborty ldquoAnintegrated D-MARCOS method for supplier selection in aniron and steel industryrdquo Decision Making Applications inManagement and Engineering vol 3 no 2 pp 49ndash69 2020

[24] E Durmic ldquoEvaluation of criteria for sustainable supplierselection using FUCOM methodrdquo Operational Research inEngineering Sciences 4eory and Applications vol 2 no 1pp 91ndash107 2019

[25] L Xiao S Zhang G Wei et al ldquoGreen supplier selection insteel industry with intuitionistic fuzzy Taxonomy methodrdquoJournal of Intelligent amp Fuzzy Systems vol 39 no 5pp 7247ndash7258 2020

[26] F Lei G Wei J Wu C Wei and Y Guo ldquoQUALIFLEXmethod for MAGDM with probabilistic uncertain linguisticinformation and its application to green supplier selectionrdquoJournal of Intelligent amp Fuzzy Systems vol 39 no 5pp 6819ndash6831 2020

[27] C Lai X Chen X Chen Z Wang X Wu and S Zhao ldquoAfuzzy comprehensive evaluation model for flood risk based on

the combination weight of game theoryrdquo Natural Hazardsvol 77 no 2 pp 1243ndash1259 2015

[28] F Franceschini M Galetto D Maisano andL Mastrogiacomo ldquoPrioritisation of engineering character-istics in QFD in the case of customer requirements orderingsrdquoInternational Journal of Production Research vol 53 no 13pp 3975ndash3988 2014

[29] M Zairi and D Ginn ldquoEast meets West a critical analysis onthe evolution growth and transfer of QFD from Japan to theWestrdquo Asian Journal on Quality vol 4 no 1 pp 1ndash19 2003

[30] A Kapur L Potters and L B Mallalieu ldquoWE-C-214-02 six-sigma tools for a ldquoNo-Flyrdquo patient safety oriented quality-checklist driven paperless multi-center radiation medicinedepartmentrdquo Medical Physics vol 38 no 6 p 3807 2011

[31] C E Shannon ldquoA mathematical theory of communicationrdquoBell System Technical Journal vol 27 no 3 pp 379ndash423 1948

[32] L-h Li and R Mo ldquoProduction task queue optimizationbased on multi-attribute evaluation for complex productassembly workshoprdquo PloS One vol 10 no 9 Article IDe0134343 2015

[33] A Liu S Luo J Mou and H Qiu ldquoe antagonism andcohesion of the upstream supply chain under informationasymmetryrdquo Annals of Operations Research pp 1ndash46 2021

[34] Y He H Guo M Jin and P Ren ldquoA linguistic entropyweight method and its application in linguistic multi-attributegroup decision makingrdquo Nonlinear Dynamics vol 84 no 1pp 399ndash404 2016

[35] R B Myerson Game 4eory Harvard University PressCambridge MA USA 2013

[36] J Von Neumann and O Morgenstern 4eory of Games andEconomic Behavior (commemorative edition) PrincetonUniversity Press Princeton NJ USA 2007

[37] J F Nash ldquoEquilibrium points in n-person gamesrdquo Pro-ceedings of the National Academy of Sciences vol 36 no 1pp 48-49 1950

[38] J Nash ldquoNon-cooperative gamesrdquo 4e Annals of Mathe-matics vol 54 no 2 pp 286ndash295 1951

[39] M M Gupta ldquoFuzzy set theory and its applicationsrdquo FuzzySets and Systems vol 47 no 3 pp 396-397 1992

[40] C Babbar and S H Amin ldquoA multi-objective mathematicalmodel integrating environmental concerns for supplier se-lection and order allocation based on fuzzy QFD in beveragesindustryrdquo Expert Systems with Applications vol 92 pp 27ndash382018

[41] J Lu S Zhang J Wu and Y Wei ldquoCOPRAS method formultiple attribute group decision making under picture fuzzyenvironment and their application to green supplier selec-tionrdquo Technological and Economic Development of Economyvol 27 no 2 pp 369ndash385 2021

[42] G Wei J Wu Y Guo J Wang and C Wei ldquoAn extendedCOPRAS model for multiple attribute group decision makingbased on single-valued neutrosophic 2-tuple linguistic envi-ronmentrdquo Technological and Economic Development ofEconomy vol 27 no 2 pp 353ndash368 2021

[43] M Zhao G Wei C Wei and Y Guo ldquoCPT-TODIMmethodfor bipolar fuzzy multi-attribute group decision making andits application to network security service provider selectionrdquoInternational Journal of Intelligent Systems vol 36 no 5pp 1943ndash1969 2021


in the management engineering and many other fields [4]Compared with other tools game theory better deals withthe common disequilibrium in reality and more effectivelymakes individual and collective rationality converge underthe condition of incomplete information and imperfectcompetition In addition game theory provides a replicabletemplate for solving complex interactions between contra-dictory subjects in the process of complex modeling whichis conducive to finding the optimal solution for all parties Itworks well when two or more players have a conflict ofinterest Similarly because the subjective weighting methodis affected by human factors while the objective weightingmethod is absolutely objective there is a big difference in theweight coefficient determined by the two methods for thesame evaluation index Game theory seeks the consistency orcompromise of its correlation weight values in fully con-sidering the foundation of the characteristics of the sub-jective and objective weight method so as to minimize thedeviation of the subjective and objective weight In theprocess they can be regarded as the two sides with conflict ofinterest while the comprehensive weight is regarded as thebenefit combination of the game erefore the compre-hensive weight based on Nash equilibrium is obtained andapplied to rational supplier selection In this paper a rationalweightingmodel combining with game theory is proposed toevaluate and select the most suitable suppliers Consideringboth decision-makersrsquo preferences and suppliersrsquo capabil-ities the subjective and objective weight of supplier evalu-ation criteria are developed for supplier selection with QFDand entropy weight Among them a two-phase fuzzy QFDmethod combined with TFN is creatively used to realize thecomplicated conversion processemost critical step gametheory is employed to combine the advantages of thesubjective and objective weight by which the comprehensiveweight can be determined e structure of the proposedmodel is shown in Figure 1

e remainders of the paper are organized as followsSection 2 is literature review Section 3 introduces thepreliminaries involved in the paper e proposed fusionmodel based on two-phase fuzzy QFD entropy weight andgame theory is introduced in Section 4 Section 5 demon-strates a numerical example to illustrate the effectiveness ofthe proposed model Section 6 makes comparative analysisand sensitivity analysis e final research conclusions arepresented in Section 7

2 Literature Review

Supplier selection is of great significance to the core com-petitiveness of manufacturing enterprises [5] Choosingsuitable suppliers is not only beneficial to reduce inventorycosts and transaction costs but also improve the orderfulfillment rate At the same time information technologyand incentive mechanism are implemented to enable en-terprises and suppliers to become a community of interestsand a rapid reaction system is established in order to shortenthe procurement cycle and make an agile response to marketdemand e common methods and related literature ofsupplier multicriteria evaluation are shown in Table 1

ere are many studies on supplier evaluation and se-lection for manufacturing enterprises Dweiri et al putforward the decision support model of supplier selection inAHP and further carried out sensitivity analysis to test therobustness of supplier selection decision [6] Starting fromthe concept of elasticity Ahmadi et al used AHP to calculatethe weight of sustainable development criteria and inter-feron gamma release assay to rank suppliers and proposed astructured and integrated evaluation decision model forsustainable suppliers in telecommunications industry [7]Zavadskas et al used fuzzy AHP to evaluate and select rawmaterial suppliers for pipeline production [8] Ayag andSamanlioglu comprehensively considered the influence ofquantitative and qualitative factors on supplier selection andproposed an intelligent solution method for the supplierselection problem based on fuzzy ANP [9] Yazdani et alsolved the relationship between customer demands withdecision-making trial and evaluation laboratory (DEMA-TEL) and then determined the degree of relationship be-tween each pair of supplier criteria and customer demandsby the QFD [10] Lima-Junior et al used fuzzy QFD toweight each indicator and then evaluated the degree ofdifficulty of supply to obtain information for each indicatorevaluation [11] Karsak and Dursun proposed a fuzzymulticriteria group decision-making method for supplierselection based on QFD fuzzy information fusion andbinary language representationmodel [12] Gupta and Baruaused BWM to rank selection criteria and then used fuzzyTOPSIS to rank the weight of supplier selection criteriaaiming to select suppliers based on the green innovationability of small- and medium-sized enterprises [13] Rezaeiet al combined with screening and BWM and developed athree-phase supplier selection method [14] Pitchipoo et aladopted grey relational analysis (GRA) as performanceindicators to determine the optimal suppliers then used theprincipal component analysis and entropy weight method toevaluate the corresponding weight values of each perfor-mance indicators and proposed an optional decision-making model to evaluate the relative performance ofsuppliers with multiple outputs and inputs [15] Badi andPamucar applied the mixed grey theory and Marcos methodin a steel companyrsquos supplier selection decision to help itimprove competitiveness [16] Govindan and Sivakumarused the fuzzy technology of similarity ranking with fuzzyTOPSIS to evaluate and select potential suppliers andproposed a model to support the selection of the best greensuppliers and the order allocation among potential suppliers[17] Mousakhani et al took into account the opinions ofpriority experts on the relative importance of criteria cal-culated the weight of decision makers with the extendedinterval-2 fuzzy TOPSIS method sorted the potential al-ternatives according to the interval-2 fuzzy hamming dis-tance measure and proposed a green supplier selectionmodel based on the group decision method [18] Blagojevicet al established a comprehensive entropy fuzzy pivotpairwise relative criteria importance assessment-data en-velopment analysis (PIPRECIA-DEA) model to study howto determine the security state of BampH under particularuncertainty conditions [19] Wei et al obtained the optimal














Define entropy

Entro

py w

eigh

t

Two-

phas

e fuz

zy Q

FD m

etho

d

Gam

e the
















E minus1

ln m1113944

m

i1pi ln pi (1)




F (x)

1

0 a1 a2 a3 a4 x

(F)The relationship



Suppliercapacities



Phase 1

Phase 2

Custo

mer

dem

ands

Man

ufac

ture

rte

chni

ques


or methods

(E)The customer

benchmark

(A)The needs of

customers




expectations

(a)

(b) (c)






F(x)

x minus a1


1 if x isin a2 a31113858 1113857

a4 minus x


0 otherwise


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)





Qi 14

1113944

4

a1fa i 1 2 m a 1 2 3 and 4 (3)



(4)




B

b11 b1n

⋮ ⋱ ⋮


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (5)




(6)



(7)


Ei minush 1113944n


where

h 1

ln n

dij cij

1113936nj1cij

(9)



WEi 1 minus Ei


(10)

where

1113944

m




vt ut

ut s1 s2 sm( 1113857

1113944

m

i1si 1

(12)


Z 1113944t1

ctvTt ct gt 0 (13)


Min Z minus ut

2

1113944t1

ctvTt minus u

Tt

2

(14)


1113944t1


Tt (15)

equivalent to


T2


T2

⋮ ⋮ ⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

c1

c2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u2 middot uT2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(16)


clowastt

ct

1113936t1ct

(17)


Zlowast

1113944t1

clowastt v

Tt (18)





EL

0 1 2 3 4 5 6 7 8 9


Medium

Medium low

Medium high

Extreme high

ML (1 2 3 4)

M (3 4 5 6)

MH (5 6 7 8)

EH (7 8 9 9)

ML MHM







cwn 1


(19)




cwn 1


(20)




B

0953 0945 0872 0846 0935 0862 0820

0012 0014 0010 0013 0013 0010 0015

1500 1850 1300 1800 1750 1200 2200

0693 0610 0782 0759 0620 0792 0735

0550 0612 0657 0604 0622 0667 0550

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)


C

1000 0940 0391 0195 0865 0316 0

0600 0200 1000 0400 0400 1000 0

0700 0350 0900 0400 0450 1000 0

0456 0 0945 0819 0055 1000 0687

0 0530 0915 0462 0615 1000 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(22)


E1 0844 E2 0853 E3 0880 E4 0836 andE5 0804









A 953 120 150 693 550B 945 140 185 610 612C 872 100 130 782 657D 846 130 180 759 604E 935 130 175 620 622F 862 100 120 792 667G 820 150 220 735 550





(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)






MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)





WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References



























































Define entropy

Entro

py w

eigh

t

Two-

phas

e fuz

zy Q

FD m

etho

d

Gam

e the
















E minus1

ln m1113944

m

i1pi ln pi (1)




F (x)

1

0 a1 a2 a3 a4 x

(F)The relationship



Suppliercapacities



Phase 1

Phase 2

Custo

mer

dem

ands

Man

ufac

ture

rte

chni

ques


or methods

(E)The customer

benchmark

(A)The needs of

customers




expectations

(a)

(b) (c)






F(x)

x minus a1


1 if x isin a2 a31113858 1113857

a4 minus x


0 otherwise


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)





Qi 14

1113944

4

a1fa i 1 2 m a 1 2 3 and 4 (3)



(4)




B

b11 b1n

⋮ ⋱ ⋮


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (5)




(6)



(7)


Ei minush 1113944n


where

h 1

ln n

dij cij

1113936nj1cij

(9)



WEi 1 minus Ei


(10)

where

1113944

m




vt ut

ut s1 s2 sm( 1113857

1113944

m

i1si 1

(12)


Z 1113944t1

ctvTt ct gt 0 (13)


Min Z minus ut

2

1113944t1

ctvTt minus u

Tt

2

(14)


1113944t1


Tt (15)

equivalent to


T2


T2

⋮ ⋮ ⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

c1

c2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u2 middot uT2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(16)


clowastt

ct

1113936t1ct

(17)


Zlowast

1113944t1

clowastt v

Tt (18)





EL

0 1 2 3 4 5 6 7 8 9


Medium

Medium low

Medium high

Extreme high

ML (1 2 3 4)

M (3 4 5 6)

MH (5 6 7 8)

EH (7 8 9 9)

ML MHM







cwn 1


(19)




cwn 1


(20)




B

0953 0945 0872 0846 0935 0862 0820

0012 0014 0010 0013 0013 0010 0015

1500 1850 1300 1800 1750 1200 2200

0693 0610 0782 0759 0620 0792 0735

0550 0612 0657 0604 0622 0667 0550

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)


C

1000 0940 0391 0195 0865 0316 0

0600 0200 1000 0400 0400 1000 0

0700 0350 0900 0400 0450 1000 0

0456 0 0945 0819 0055 1000 0687

0 0530 0915 0462 0615 1000 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(22)


E1 0844 E2 0853 E3 0880 E4 0836 andE5 0804









A 953 120 150 693 550B 945 140 185 610 612C 872 100 130 782 657D 846 130 180 759 604E 935 130 175 620 622F 862 100 120 792 667G 820 150 220 735 550





(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)






MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)





WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References

























































E minus1

ln m1113944

m

i1pi ln pi (1)




F (x)

1

0 a1 a2 a3 a4 x

(F)The relationship



Suppliercapacities



Phase 1

Phase 2

Custo

mer

dem

ands

Man

ufac

ture

rte

chni

ques


or methods

(E)The customer

benchmark

(A)The needs of

customers




expectations

(a)

(b) (c)






F(x)

x minus a1


1 if x isin a2 a31113858 1113857

a4 minus x


0 otherwise


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)





Qi 14

1113944

4

a1fa i 1 2 m a 1 2 3 and 4 (3)



(4)




B

b11 b1n

⋮ ⋱ ⋮


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (5)




(6)



(7)


Ei minush 1113944n


where

h 1

ln n

dij cij

1113936nj1cij

(9)



WEi 1 minus Ei


(10)

where

1113944

m




vt ut

ut s1 s2 sm( 1113857

1113944

m

i1si 1

(12)


Z 1113944t1

ctvTt ct gt 0 (13)


Min Z minus ut

2

1113944t1

ctvTt minus u

Tt

2

(14)


1113944t1


Tt (15)

equivalent to


T2


T2

⋮ ⋮ ⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

c1

c2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u2 middot uT2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(16)


clowastt

ct

1113936t1ct

(17)


Zlowast

1113944t1

clowastt v

Tt (18)





EL

0 1 2 3 4 5 6 7 8 9


Medium

Medium low

Medium high

Extreme high

ML (1 2 3 4)

M (3 4 5 6)

MH (5 6 7 8)

EH (7 8 9 9)

ML MHM







cwn 1


(19)




cwn 1


(20)




B

0953 0945 0872 0846 0935 0862 0820

0012 0014 0010 0013 0013 0010 0015

1500 1850 1300 1800 1750 1200 2200

0693 0610 0782 0759 0620 0792 0735

0550 0612 0657 0604 0622 0667 0550

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)


C

1000 0940 0391 0195 0865 0316 0

0600 0200 1000 0400 0400 1000 0

0700 0350 0900 0400 0450 1000 0

0456 0 0945 0819 0055 1000 0687

0 0530 0915 0462 0615 1000 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(22)


E1 0844 E2 0853 E3 0880 E4 0836 andE5 0804









A 953 120 150 693 550B 945 140 185 610 612C 872 100 130 782 657D 846 130 180 759 604E 935 130 175 620 622F 862 100 120 792 667G 820 150 220 735 550





(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)






MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)





WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References


















































F(x)

x minus a1


1 if x isin a2 a31113858 1113857

a4 minus x


0 otherwise


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)





Qi 14

1113944

4

a1fa i 1 2 m a 1 2 3 and 4 (3)



(4)




B

b11 b1n

⋮ ⋱ ⋮


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠ (5)




(6)



(7)


Ei minush 1113944n


where

h 1

ln n

dij cij

1113936nj1cij

(9)



WEi 1 minus Ei


(10)

where

1113944

m




vt ut

ut s1 s2 sm( 1113857

1113944

m

i1si 1

(12)


Z 1113944t1

ctvTt ct gt 0 (13)


Min Z minus ut

2

1113944t1

ctvTt minus u

Tt

2

(14)


1113944t1


Tt (15)

equivalent to


T2


T2

⋮ ⋮ ⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

c1

c2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u2 middot uT2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(16)


clowastt

ct

1113936t1ct

(17)


Zlowast

1113944t1

clowastt v

Tt (18)





EL

0 1 2 3 4 5 6 7 8 9


Medium

Medium low

Medium high

Extreme high

ML (1 2 3 4)

M (3 4 5 6)

MH (5 6 7 8)

EH (7 8 9 9)

ML MHM







cwn 1


(19)




cwn 1


(20)




B

0953 0945 0872 0846 0935 0862 0820

0012 0014 0010 0013 0013 0010 0015

1500 1850 1300 1800 1750 1200 2200

0693 0610 0782 0759 0620 0792 0735

0550 0612 0657 0604 0622 0667 0550

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)


C

1000 0940 0391 0195 0865 0316 0

0600 0200 1000 0400 0400 1000 0

0700 0350 0900 0400 0450 1000 0

0456 0 0945 0819 0055 1000 0687

0 0530 0915 0462 0615 1000 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(22)


E1 0844 E2 0853 E3 0880 E4 0836 andE5 0804









A 953 120 150 693 550B 945 140 185 610 612C 872 100 130 782 657D 846 130 180 759 604E 935 130 175 620 622F 862 100 120 792 667G 820 150 220 735 550





(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)






MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)





WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References















































WEi 1 minus Ei


(10)

where

1113944

m




vt ut

ut s1 s2 sm( 1113857

1113944

m

i1si 1

(12)


Z 1113944t1

ctvTt ct gt 0 (13)


Min Z minus ut

2

1113944t1

ctvTt minus u

Tt

2

(14)


1113944t1


Tt (15)

equivalent to


T2


T2

⋮ ⋮ ⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

c1

c2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u2 middot uT2

⋮

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(16)


clowastt

ct

1113936t1ct

(17)


Zlowast

1113944t1

clowastt v

Tt (18)





EL

0 1 2 3 4 5 6 7 8 9


Medium

Medium low

Medium high

Extreme high

ML (1 2 3 4)

M (3 4 5 6)

MH (5 6 7 8)

EH (7 8 9 9)

ML MHM







cwn 1


(19)




cwn 1


(20)




B

0953 0945 0872 0846 0935 0862 0820

0012 0014 0010 0013 0013 0010 0015

1500 1850 1300 1800 1750 1200 2200

0693 0610 0782 0759 0620 0792 0735

0550 0612 0657 0604 0622 0667 0550

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)


C

1000 0940 0391 0195 0865 0316 0

0600 0200 1000 0400 0400 1000 0

0700 0350 0900 0400 0450 1000 0

0456 0 0945 0819 0055 1000 0687

0 0530 0915 0462 0615 1000 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(22)


E1 0844 E2 0853 E3 0880 E4 0836 andE5 0804









A 953 120 150 693 550B 945 140 185 610 612C 872 100 130 782 657D 846 130 180 759 604E 935 130 175 620 622F 862 100 120 792 667G 820 150 220 735 550





(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)






MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)





WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References



















































cwn 1


(19)




cwn 1


(20)




B

0953 0945 0872 0846 0935 0862 0820

0012 0014 0010 0013 0013 0010 0015

1500 1850 1300 1800 1750 1200 2200

0693 0610 0782 0759 0620 0792 0735

0550 0612 0657 0604 0622 0667 0550

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(21)


C

1000 0940 0391 0195 0865 0316 0

0600 0200 1000 0400 0400 1000 0

0700 0350 0900 0400 0450 1000 0

0456 0 0945 0819 0055 1000 0687

0 0530 0915 0462 0615 1000 0

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(22)


E1 0844 E2 0853 E3 0880 E4 0836 andE5 0804









A 953 120 150 693 550B 945 140 185 610 612C 872 100 130 782 657D 846 130 180 759 604E 935 130 175 620 622F 862 100 120 792 667G 820 150 220 735 550





(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)






MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)





WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References


















































(21600 3040042600 48800)

(23800 3200044600 51800)

(21600 3040042600 48800)

(39400 5280068200 74200)

(24600 3280045400 52000)

(40600 5440070200 75600)






MT1 (0012) (7899) (1234) (0012) (0012) (21600 3040042600 48800)

MT2 (0012) (7899) (0012) (1234) (0012) (23800 3200044600 51800)

MT3 (7899) (0012) (5678) (7899) (0012) (21600 3040042600 48800)

MT4 (3456) (5678) (3456) (5678) (7899) (39400 5280068200 74200)

MT5 (7899) (0012) (5678) (7899) (0012) (24600 3280045400 52000)

MT6 (5678) (5678) (7899) (5678) (7899) (40600 5440070200 75600)

cwn cw1 cw2 cw3 cw4 cw5(107433 173867285267 359733)

(119633 190400306933 384233)

(109167 181067293533 371800)

(124533 202133322867 401733)

(93333 142933236800 291833)





WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References
















































WE1 0199 WE2 0188 WE3 0153 WE4 0209and WE5 0250



v1 (0197 0213 0203 0224 0163) and v2 (01990188 0153 0209 0250)



c c1 c21113858 1113859 [0398 0615] (23)


clowast

clowast1 clowast21113858 1113859 [0393 0607]

Zlowast

[0198 0198 0173 0215 0216](24)












026

024

022

02

018

016

1 2 3 4 5


Wei

ght v

alue



0 01

088086084082

08078076074072

07068


Scor

e

09 1






7 Conclusions






Data Availability




Acknowledgments


References
















































7 Conclusions






Data Availability




Acknowledgments


References















































Rational Supplier Selection Based on Two-Phase Deep ...

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