An Application of Fuzzy Integrated Model in Green Supplier

Research ArticleAn Application of Fuzzy Integrated Model inGreen Supplier Selection

Alptekin UlutaG 1 AyGe Topal2 and Rim Bakhat3

1Department of International Trade and Logistics Faculty of Economics and Administrative SciencesSivas Cumhuriyet University Sivas 58140 Turkey2Department of Business Faculty of Economics and Administrative Sciences Nigde Omer Halisdemir University Nigde 51240 Turkey3Department of Economics and Social Sciences University Abdel Malek Essadi Tangier-Tetouan 93030 Morocco

Correspondence should be addressed to Alptekin Ulutas aulutascumhuriyetedutr

Received 7 March 2019 Accepted 8 April 2019 Published 18 April 2019

Academic Editor Anna M Gil-Lafuente

Copyright copy 2019 Alptekin Ulutas et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

ldquoSustainabilityrdquo term has not only become increasingly important globally for individual companies but also become importantfor whole supply chains The selection of supplier is a significant decision for the sustainability of supply chains Literature reviewrevealed that supplier selection is made traditionally based on economic attributes which are insufficient for sustainability of supplychains as sustainability requires taking economic environmental and social issues into account For this purpose this paperproposes determining the green supplier selection attributes and then developing a methodology for assessment and ranking ofgreen suppliers based on determined attributes The first contribution of this study is to propose a novel method which is FROV(fuzzy extension of range of value) to literatureThe latter is to utilize fuzzy extension of preference selection index (FPSI) to identifythe weights of attributes The third is to develop a novel fuzzy multiattribute decision-making model consisting of FPSI and FROVto determine the best supplier for a Turkish textile company

1 Introduction

ldquoSustainable Developmentrdquo has become increasingly impor-tant globally in recent decades The World Commission onEnvironment and Development [1] explained ldquoSustainableDevelopmentrdquo as supplying resources for meeting the needsof people currently livingwithoutmaking a significant impacton the resources needed for people living in the future inOur Common Future report It is suggested in the reportthat effective long-term development will be successful ifeconomic environmental and social concerns will be takeninto consideration

Numerous studies have shown that with the entry ofsustainability into plans and policies meeting environmentaland social goals together with economic goals has beenimportant not only for government sector but also for privatesector such as construction [2ndash5] fisheries [6ndash11] mining[12ndash17] and transportation [18ndash24]

Despite the studies above discussing sustainability inthe scale of individual companies Vachon and Klassen [51]

suggested that the environmental management should notbe restricted to the individual companies alone and must gofurther to the whole supply chain involving all companiesthroughout the entire life of product For this purpose theperception of GSCM (Green Supply Chain Management)appeared in the literature during the 1990s when competitionhad an increasing trend [52] GSCM is defined as incorporat-ing environmental or green concerns into the supply chainprocesses beginning from design of the product to recyclingof the goods at the end of its life [53]

Traditionally supplier selection has a crucial role insupply chains as it contributes to increasing product qualityand customer satisfaction [54] It has becomemore importantand complex with recent trends sustainability developmentandGSCMTherefore developing amodel for selecting greensuppliers is necessary for maintaining sustainability in asupply chain The process of supplier selection in traditionalsupply chains has been named as green supplier selection inGSCM and became a central part of GSCM [55]

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 4256359 11 pageshttpsdoiorg10115520194256359

2 Mathematical Problems in Engineering

Table 1 The most common used economic attributes in supplier selection

Quality Financial PerformanceDelivery (Time) Management and OrganizationPrice Production Facilities and CapacityFlexibility ReliabilityTechnical Capability Long-term RelationshipSources [25ndash37]

For this purpose this paper proposes determining thegreen attributes for the selection of supplier and then devel-oping a model for assessing and ordering of green suppliersbased on determined attributes Three contributions havebeen made into the literature by this paper The first is topropose a novel model which is fuzzy extension of rangeof value (FROV) to literature Generally fuzzy extension ofpreference selection index (FPSI) has not been applied toacquire attribute weights so the second is to utilize FPSI toidentify the weights of attributes The third is to develop anovel fuzzy multiattribute decision-making (MADM) modelconsisting of FPSI and FROV to address supplier selectionproblem for a Turkish textile company

The rest of the paper is organized as follows After theintroduction the attributes used for selecting green supplierin the literature are reviewed in Section 2 Then the novelmodel is explained in detail in Section 3 In Section 4the results are presented and the results of FROV arecompared with the results of other fuzzy MADM which arefuzzy additive ratio assessment (ARAS) [56] fuzzy multipleobjective optimization on the basis of ratio analysis plus fullmultiplicative form (MULTIMOORA) [57] fuzzy complexproportional assessment (COPRAS) [58] and fuzzy greyrelational analysis (GRA) [59] In Section 5 a sensitivityanalysis is done in order to observe the changing of the resultswith respect to the changing of attribute weights In Section 6a brief conclusion is presented

2 Literature Review

In the literature review section attributes utilized for greensupplier selection in the literature have been reviewed todetermine which attributes to be used in the model (Sec-tion 3) There are three groups of attributes in the literatureused for green supplier selection economic environmentaland social Environmental and social attributes are addressedas green attributes in this section

21 Economic Attributes Economic attributes have beenused commonly for a long time in supplier selection beforesustainability introduced to supply chain management [25]The economic attributes mostly used for supplier selectionwere summarized in Table 1

Due to the profit maximization objectives of firms priceattribute was once the most popular economic attribute usedin supplier selection [26 27] However it was shown thatprice attribute alone is insufficient for supplier selectionproblems in the literature review conducted by Ho et al [28]The review presented that quality delivery management

technology relationship and flexibility attributes are also sig-nificant in supplier selection besides price attribute Financialperformance attribute is deemed significant by Buyukozkanand Cifci [29] and Dickson [30] as it shows the stability andthus the continuity of supplier firms Dickson [30] presentedthe importance of production capacity in addition to theattributes mentioned above Kannan et al [31] indicated thatreliability attribute is among most common used traditionalattributes in the literature

As it is seen in the literature economic attributes arethe main focus for traditional supplier selection Howeverrecent changes in the economy and politics such as increasingcompetition and foreign trade consumers and governmentsgiving more importance to sustainability therefore requiredenvironmental and social attributes to be included in supplierselection

22 Green Attributes Several studies in the literatureaddressed the green attributes (social and environmental) insupplier selection problems Table 2 summarizes the greenattributes used in the literature

Noci [38] presented a supplier selection model basedon environmental performance of suppliers It was claimedthat increasing concerns about environmental performanceof corporates will lead the corporates to choose suppliersbased on an environmental viewpoint Handfield et al [39]presented an analytic hierarchy process (AHP) based supplierselection model to be used in the selection of suppliersbased on environmental responsibility attribute Humphreyset al [40] introduced a supplier selection decision-makingmodel by using Knowledge-Based System (KBS) which usedqualitative and quantitative environmental attributes

Lee et al [32] developed an integrated model includ-ing fuzzy AHP and Delphi methods to choose the mostappropriate green suppliers for corporations Kuo et al[33] created green supplier selection model by integratingthe artificial neural network (ANN) the data envelopmentanalysis (DEA) and analytic network process (ANP)

Buyukozkan and Cifci [41] conducted a study to eval-uate the sustainability of suppliers with ANP Kannan etal [42] selected suppliers based on economic and envi-ronmental attributes in their model integrating fuzzy AHPfuzzy technique for order preference by similarity to idealsolution (TOPSIS) multiobjective linear programming andfuzzy logic Hashemi et al [43] suggested a comprehensivegreen supplier selection model by using ANP the traditionalGRA and both economic and environmental attributesRostamzadeh et al [44] presented a model for evaluatinggreen suppliers based on quantitative data by using fuzzy sets

Mathematical Problems in Engineering 3

Table 2 Green attributes used in supplier selection

ATTRIBUTES(i) Using green technologies(ii) Environmental efficiency(iii) Supplierrsquos green image(iv) Reverse logistics (recycling remanufacturing reusing)(v) Reducing activities(i) Pollution level(ii) Waste management(iii) Noise(iv) Resource consumption (energy material water)(i) Green packaging and labelling(ii) Green transportation(iii) Green product design(iv) Green procurement(v) Green warehousing(vi) Green innovation and RampD(vii) Green stock politics(i) Occupational health and safety systems(ii) Social responsibility(iii) Employeesrsquo interests and rights(iv) The stakeholdersrsquo rightsSources [32ndash34 38ndash50]

Table 3 Linguistic and fuzzy performance ratings

Linguistic Performance Ratings Fuzzy Performance RatingsVery Strong (7910)Strong (579)Moderate (357)Weak (135)Very Weak (013)

theory and the Vlsekriterijumska Optimizacija I Kompro-misno Resenje (VIKOR) method

Awasthi and Kannan [45] developed an integrated deci-sion approach to analyse and select development programsfor green suppliers by using a fuzzy nominal group technique(NGT) and VIKOR Uygun and Dede [46] provided anintegrated fuzzymodel including fuzzy decision-making trialand evaluation laboratory (DEMATEL) method ANP andfuzzy TOPSIS to analyse green performances of companiesin supply chains Chen et al [60] proposed fuzzy AHP andfuzzy TOPSIS to solve green supplier selection problem Panget al [61] proposed a fuzzy grey model to address greensupplier selection problem Guo et al [47] presented a frame-work including the triple bottom line principle and fuzzyaxiomatic design (AD) technique to solve green supplierselection problem in global apparel industry Luthra et al [34]provided a framework selecting suppliers in accordance withsustainability by using a model integrating AHP and VIKORmethods They identified 22 economic environmental andsocial attributes Wang et al [48] developed a frameworkfor selecting green suppliers by using the cloud model and

qualitative flexible multiple criteria method (QUALIFLEX)with the economic and environmental attributes

Vahidi et al [49] developed a novel possibilistic-stochastic model for the selection of sustainable suppliers Itshowed that sustainability is significant in terms of reducingsupply costs Yu et al [50] presented a model for selectinggreen suppliers based on carbon footprints Yucesan etal [62] combined the best-worst method (BWM) and theinterval type 2 fuzzy TOPSIS methods to solve green supplierselection problem

3 Methodology

Maniya and Bhatt [63] introduced preference selection index(PSI) to solve material selection problem The range of value(ROV) was developed by Yakowitz et al [64] The ROVmethod is one of the scoring methods The easiest MADMmethods are scoringmethods [65]However there are limitedstudies related to ROV method in the literature While mostof these studies were using the crisp ROVmethod Zavadskaset al [66] developed the rough ROV method In this studyFPSI and FROV are used to select the best supplier byconsidering environmental aspects FPSI is used to identifythe objective weights of attributes and FROV is used toorder the suppliers with respect to their performancesMethodology section consists of three subsections includingfuzzy arithmetic operations FPSI and FROV methods

31 Fuzzy Arithmetic Operations It can be supposed thatthe arithmetic operations are used for the fuzzy numbersand crisp numbers 119866 = (119892119897 119892119898 119892119906) and = (ℎ119897 ℎ119898 ℎ119906)represent the two positive triangular fuzzy numbers Moredetails are indicated as follows [67]

(i) Addition 119866 + = (119892119897 + ℎ119897 119892119898 + ℎ119898 119892119906 + ℎ119906)(ii) Subtraction 119866 minus = (119892119897 minus ℎ119897 119892119898 minus ℎ119898 119892119906 minus ℎ119906)(iii) Multiplication 119866 times = (min (119892119897ℎ119897 119892119897ℎ119906 119892119906ℎ119897 119892119906ℎ119906)119892119898ℎ119898 max (119892119897ℎ119897 119892119897ℎ119906 119892119906ℎ119897 119892119906ℎ119906))(iv) Division 119866 = (min (119892119897ℎ119897 119892119897ℎ119906 119892119906ℎ119897 119892119906ℎ119906)119892119898ℎ119898 max (119892119897ℎ119897 119892119897ℎ119906 119892119906ℎ119897 119892119906ℎ119906))

The e represents a positive crisp number [68](v) Scalar division 119866119890 = (119892119897119890 119892119898119890 119892119906119890)

32 Fuzzy Preference Selection Index FPSI method consistsof five steps which are explained as follows

Step 1-1 Decision-makers used Table 3 to assign linguisticperformance rating Fuzzy performance rating of decision-makers is aggregated by using (1) to structure aggregatedfuzzy decision matrix (D)

119889119894119895 = 1119870119870sum119896=1

119889119894119895119896 (1)

In (1) 119889119894119895119896 denotes 119896th decision-makerrsquos fuzzy perfor-mance rating (119889119894119895) and 119889119894119895 is fuzzy performance rating of


119894th alternative on 119895th attribute and it is an element of 119863 =[119889119894119895]119898times119899Step 1-2 After structuring aggregated fuzzy decision matrixthe normalized fuzzy performance rating (119894119895) which is anelement of normalized fuzzy decision matrix ( = [119894119895]119898times119899)is calculated by using (2) (beneficial attributes) and (3)(nonbeneficial attributes) indicated as follows

119894119895 = 119889119894119895max (119889119894119895) (2)

119894119895 = min (119889119894119895)119889119894119895 (3)

Step 1-3 The averaged fuzzy normalized value (119894119895) of eachattribute is computed by

119894119895 = 1119898119898sum119894=1

119894119895 (4)

Step 1-4 The fuzzy preference value (119875119881119895 =(119875119881119897119895 119875119881119898119895 119875119881119906119895 )) of each attribute is calculated as follows

119875119881119895 = 119898sum119894=1

(119894119895 minus 119894119895)2 (5)

Step 1-5 The fuzzy deviation value (119895) of each attribute iscomputed by (6) Then fuzzy weight (119908119895) of each attributeis calculated by (7) and fuzzy normalized weight (119908lowast119895 ) iscomputed by (8)

119895 = (120590119897119895 120590119898119895 120590119906119895 ) = 100381610038161003816100381610038161 minus 11987511988111989510038161003816100381610038161003816= (100381610038161003816100381610038161 minus 119875119881119906119895 10038161003816100381610038161003816 100381610038161003816100381610038161 minus 119875119881119898119895 10038161003816100381610038161003816 100381610038161003816100381610038161 minus 11987511988111989711989510038161003816100381610038161003816)

(6)

119908119895 = 119895sum119899119895=1 119895 (7)

119908lowast119895 = 3 times 119908119895sum119899119895=1 119908119897119895 + sum119899119895=1 119908119898119895 + sum119899119895=1 119908119906119895 (8)

After obtaining the fuzzy normalizedweight of each attributethese weights are transferred into FROV method

33 Fuzzy Range of Value FROVmethod contains four stepsindicated as follows

Step 2-1 The range of fuzzy values placed in the aggregatedfuzzy decision matrix (119863) which is structured in (1) is

obtained by (9) (beneficial attributes) and (10) (nonbeneficialattributes)

119904119894119895 = 119889119894119895 minusmin (119889119894119895)max (119889119894119895) minusmin (119889119894119895)

= ( 119889119897119894119895 minusmin (119889119906119894119895)max (119889119897119894119895) minusmin (119889119897119894119895) 119889119898119894119895 minusmin (119889119898119894119895 )

max (119889119898119894119895 ) minusmin (119889119898119894119895 ) 119889119906119894119895 minusmin (119889119897119894119895)

max (119889119906119894119895) minusmin (119889119897119894119895))

(9)

119904119894119895 = max (119889119894119895) minus 119889119894119895max (119889119894119895) minusmin (119889119894119895)

= ( max (119889119897119894119895) minus 119889119906119894119895max (119889119897119894119895) minusmin (119889119897119894119895) max (119889119898119894119895 ) minus 119889119898119894119895

max (119889119898119894119895 ) minusmin (119889119898119894119895 ) max (119889119906119894119895) minus 119889119897119894119895

max (119889119906119894119895) minusmin (119889119897119894119895))

(10)

In (9) and (10) 119904119894119895 which is an element of the fuzzy rangedecision matrix (119878 = [119904119894119895]119898times119899) indicates the range of fuzzyvalues

Step 2-2 After this fuzzy worst utility values (minus119894 ) and fuzzybest utility values (+119894 ) for each alternative are computed asfollows

minus119894 = 119891sum119894=1

119904119894119895119908119895 (11)

+119894 = 119898sum119894=119891+1

119904119894119895119908119895 (12)

Step 2-3 Fuzzy overall score (119894 = (119906119897119894 119906119898119894 119906119906119894 )) for eachalternative is calculated by

119894 = minus119894 + +1198942 (13)

Step 2-4 Fuzzy overall scores (119894) are converted into crispoverall score (119906119894) by using

119906119894 = 119906119897119894 + 119906119898119894 + 1199061199061198943 (14)

Then alternatives are ordered from the highest crispoverall score to the lowest crisp overall score The alternativehaving the highest crisp overall score is identified as the mostappropriate alternative

4 Application

The hybrid fuzzy model is applied into a textile com-pany which has more than 10 years of experience in the


Table 4 The aggregated fuzzy decision matrix

Suppliers AttributesA1 A2 A3

Supplier 1 (25332) (002000220024) (001200130014)Supplier 2 (323334) (001700210023) (001100120015)Supplier 3 (28331) (001900240025) (000900100017)Supplier 4 (293134) (001800230024) (001000110012)Supplier 5 (323335) (001600190021) (000800100015)Supplier 6 (313234) (001800210022) (001000140016)Supplier 7 (313335) (001900220023) (001000110013)Supplier 8 (323435) (001700210024) (001000120014)





sector manufacturing suits for global market The buyersof the suits motivate the company to work with greensuppliers Before interviewing with managers of companyattribute list was structured by means of literature Thenthe company managers were asked whether the attributeswere appropriate for the company in the supplier selectionprocess Nine attributes were identified for using in supplierselection These attributes are Cost (A1) Defective Rate(A2) Late Delivery Rate (A3) Technological Capability (A4)Technical Assistance (A5) Pollution Control (A6) Envi-ronmental Management (A7) Green Transportation (A8)and Green Warehousing (A9) The first three attributes areidentified as nonbeneficial attributes and the others areidentified as beneficial attributes This company procuresyarn (thread spools) from 8 suppliers The fuzzy data ofthe first three attributes were obtained from factory man-ager considering actual data of company The fuzzy dataof other attributes were collected from five managers ofcompany including factory manager purchasing managerplanning manager operation manager and quality man-ager The aggregated fuzzy decision matrix is indicated inTable 4

By using (2) and (3) the aggregated fuzzy decisionmatrix is normalized The normalized fuzzy decision matrixis demonstrated in Table 5

By means of (5) the fuzzy preference value (PVj) ofeach attribute is computed After obtaining PVj the fuzzydeviation value (j) of each attribute is calculated by using (6)Then fuzzy weight (119908119895) and fuzzy normalized weight (119908lowast119895 ) ofeach attribute is computed by using (7) and (8) respectivelyThese results are indicated in Table 6

The fuzzy weights of attributes are considered into FROVBy means of (9) and (10) the fuzzy range decision matrix (119878)which is indicated in Table 7 is calculated

In final step the fuzzy best and worst utility values(+119894 minus119894 ) of each supplier are calculated by using (11) and (12)respectively These values are aggregated by (13) to obtainfuzzy overall score (119894) for each alternative and these fuzzyscores are converted into crisp overall score (119906119894) by using (14)These results are indicated in Table 8

According to crisp overall score (119906119894) indicated in Table 8the ranking of suppliers are as follows Supplier 5 Supplier 4Supplier 6 Supplier 3 Supplier 1 Supplier 8 and Supplier 2


Table 5 The normalized fuzzy decision matrix (for FPSI)







Table 6 The results of FPSI

Results AttributesA1 A2 A3

PVj (000900150064) (001200250051) (002800730158)j (093609850991) (094909750988) (084209270972)wj (011201320156) (011401300156) (010101240153)119908lowast119895 (0109 0129 0152) (0111 0127 0152) (0099 0121 0149)


PVj (010101250126) (010601270130) (005900960185)j (087408750899) (087008730894) (081509040941)wj (010501170142) (010501160141) (009801210148)119908lowast119895 (0102 0114 0139) (0102 0113 0138) (0096 0118 0144)


PVj (014502450507) (012904221172) (008403801385)j (049307550855) (017205780871) (038506200916)wj (005901010135) (002100770137) (004600830144)119908lowast119895 (0058 0099 0132) (0020 0075 0134) (0045 0081 0141)


Table 7 The fuzzy range decision matrix


Supplier 1 (0 1 1429) (-1 0400 1250) (-0500 0250 1250)Supplier 2 (-0286 0250 0429) (-0750 0600 2) (-0750 0500 1500)Supplier 3 (0100 1 1) (-1250 0 1500) (-1250 1 2)Supplier 4 (-0286 0750 0857) (-1 0200 1750) (0 0750 1750)Supplier 5 (-0429 0250 0429) (-0250 1 2250) (-0750 1 2250)Supplier 6 (-0286 0500 0571) (-0500 0600 1750) (-1 0 1750)Supplier 7 (-0429 0250 0571) (-0750 0400 1500) (-0250 0750 1750)Supplier 8 (-0429 0 0429) (-1 0600 2) (-0500 0500 1750)


Supplier 1 (-0800 0200 1200) (-0600 0400 1400) (-1143 0286 1714)Supplier 2 (-1 0 1) (-0700 0300 1300) (-1 0429 1857)Supplier 3 (-0700 0300 1300) (-0600 0400 1400) (-1 0429 1857)Supplier 4 (-0600 0400 1400) (-1 0 1) (-0857 0571 2)Supplier 5 (-0500 0500 1500) (-0900 0100 1100) (-0429 1 2429)Supplier 6 (-0800 0200 1200) (0 1 1750) (-1143 0286 1714)Supplier 7 (-0500 0500 1500) (-0600 0400 1400) (-1143 0286 1714)Supplier 8 (0 1 1750) (-0400 0600 1550) (-1429 0 1429)


Supplier 1 (-0778 0333 1444) (-0667 0500 1667) (-0546 0875 2636)Supplier 2 (-1111 0 1111) (-1 0 1) (-1364 0 1364)Supplier 3 (-0778 0333 1444) (-0533 0600 1800) (-0727 0750 2455)Supplier 4 (-0556 0556 1667) (-0133 0900 2200) (-0909 0625 2273)Supplier 5 (-0111 1 2111) (0 1 2333) (-0364 1 2818)Supplier 6 (-0778 0333 1444) (-0400 0700 1933) (-0546 0875 2636)Supplier 7 (-1111 0 1111) (-0267 0800 2067) (-0909 0625 2273)Supplier 8 (-1111 0 1111) (-0533 0600 1800) (-0909 0625 2273)

012345678

1 2 3 4 5

Rank

ing

SetsSupplier 1Supplier 2Supplier 3Supplier 4

Supplier 5Supplier 6Supplier 7Supplier 8

Figure 1 The results of sensitivity analysis

Therefore the best supplier among 8 suppliers is identified asSupplier 5

The results of FROV are compared with the results ofother fuzzy MADM which are fuzzy ARAS fuzzy MULTI-MOORA fuzzy COPRAS and fuzzy GRA Table 9 presents

the coefficient of Spearmanrsquos correlation for all other fuzzyMADM

According to Table 9 the correlation between the resultsof FROV and the results of other fuzzy MADM methods isvery high Table 9 proves that the FROVmethod has reached


Table 8 The results of FROV

Suppliers Resultsminus119894 +119894Supplier 1 (-0227 0210 0593) (-0628 0244 1393)Supplier 2 (-0269 0169 0593) (-0853 0085 1058)Supplier 3 (-0365 0250 0678) (-0601 0269 1419)Supplier 4 (-0195 0213 0657) (-0563 0287 1456)Supplier 5 (-0215 0280 0742) (-0322 0441 1700)Supplier 6 (-0268 0141 0614) (-0510 0327 1478)Supplier 7 (-0216 0174 0576) (-0629 0247 1393)Supplier 8 (-0292 0137 0630) (-0607 0278 1371)

Suppliers Results119894 119906119894Supplier 1 (-0428 0227 0993) 0264Supplier 2 (-0561 0127 0826) 0131Supplier 3 (-0483 0260 1049) 0275Supplier 4 (-0379 0250 1057) 0309Supplier 5 (-0269 0361 1221) 0438Supplier 6 (-0389 0234 1046) 0297Supplier 7 (-0423 0211 0985) 0258Supplier 8 (-0450 0208 1001) 0253

Table 9 Spearman correlation coefficient for all fuzzy MADM

Fuzzy MADM FROV Fuzzy ARAS FuzzyMULTIMOORA Fuzzy COPRAS Fuzzy GRA

FROV 1000 0952 0929 0881 0833Fuzzy ARAS - 1000 0916 0952 0952Fuzzy MULTIMOORA - - 1000 0952 0857Fuzzy COPRAS - - - 1000 0952Fuzzy GRA - - - - 1000

the accurate results Additionally FROV method includesfew and simple steps It can easily be used to solve MADMproblems

5 Sensitivity Analysis

The sensitivity analysis is done to monitor the changing ofthe results with respect to the changing of attribute weightsFor this purpose five sets of attribute weights are determinedTable 10 presents the sets of attribute weights

These attribute weights are used to do the sensitivityanalysis The results of the sensitivity analysis are presentedin Figure 1

As it can be seen that Supplier 5 is determined as thebest supplier for Sets 1 4 and 5 nevertheless Supplier 1is identified as the best supplier in Set 2 and Supplier 6 isdetermined as the best supplier in Set 3 Only one supplierrsquosrank does not change That supplier is Supplier 2 and thissupplier is always 8th rank The ranking of other suppliersvaries at least oncewith respect to the sets of attributeweights

6 Conclusion

This studyrsquos main objective was to develop a hybrid modelto choose suppliers in accordance with sustainability and forthis purpose it made three contributions to green supplierselection literature First contribution is proposing a newmethod which is FROV to literature second contribution isutilizing FPSI to identify the weights of attributes and thirdcontribution is developing a newMADMmodel consisting ofFPSI and FROV to solve supplier selection

Choosing the most suitable attributes and the method tobe used in the decisionmodel is significant for green supplierselection Therefore first a review of attributes used in theselection was conducted and a comprehensive list of suitableattributes for selecting green suppliers was created Then aninterview was held with the managers of a textile companyto shape a final list of applicable attributes for this studyNine attributes were identified for using in supplier selectionThese attributes are Cost (A1) Defective Rate (A2) LateDelivery Rate (A3) Technological Capability (A4) Technical


Table 10 Sensitivity analysis

Attributes SetsSet 1 Set 2 Set 3

Attribute 1 (0036 0043 0051) (0370 0390 0450) (0200 0240 0450)Attribute 2 (0037 0042 0051) (0012 0014 0017) (0150 0180 0190)Attribute 3 (0033 0040 0050) (0011 0013 0017) (0020 0050 0070)Attribute 4 (0051 0057 0070) (0015 0019 0023) (0210 0220 0230)Attribute 5 (0051 0057 0069) (0017 0019 0023) (0200 0220 0260)Attribute 6 (0048 0059 0070) (0060 0080 0090) (0010 0020 0030)Attribute 7 (0029 0050 0066) (0040 0060 0070) (0020 0030 0040)Attribute 8 (0300 0320 0330) (0140 0200 0240) (0010 0020 0040)Attribute 9 (0290 0330 0370) (0140 0190 0280) (0020 0030 0040)

Attributes SetsSet 4 Set 5

Attribute 1 (0010 0030 0070) (0300 0320 0350)Attribute 2 (0020 0030 0040) (0160 0190 0200)Attribute 3 (0050 0060 0080) (0160 0180 0190)Attribute 4 (0070 0080 0090) (0050 0070 0090)Attribute 5 (0010 0020 0040) (0080 0140 0150)Attribute 6 (0120 0140 0160) (0010 0020 0040)Attribute 7 (0150 0170 0190) (0020 0030 0040)Attribute 8 (0200 0220 0230) (0020 0030 0040)Attribute 9 (0220 0249 0251) (0020 0040 0060)

Assistance (A5) Pollution Control (A6) EnvironmentalManagement (A7) Green Transportation (A8) and GreenWarehousing (A9)

In addition this study provided a novel hybrid MADMmodel to select green supplierThe proposed model incorpo-rated FPSI which is used to identify the weights of attributesand FROV which is used to order the suppliers with respectto their performances

Future studies may use this model to solve other MADMproblems such as logistics provider selection energy sourcesselection and warehouse location selection

Data Availability

All data used to support the findings of this study are includedwithin the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] WCED Our Common Future Report of the World Commissionon Environment and Development 1987

[2] F Afzal B Lim and D Prasad ldquoAn investigation of corporateapproaches to sustainability in the construction industryrdquoProcedia Engineering vol 180 pp 202ndash210 2017

[3] R-D Chang J Zuo Z-Y Zhao et al ldquoSustainability attitudeand performance of construction enterprises a china studyrdquoJournal of Cleaner Production vol 172 pp 1440ndash1451 2018

[4] R-H Chen Y Lin and M-L Tseng ldquoMultiattributes analysisof sustainable development indicators in the constructionminerals industry in Chinardquo Resources Policy vol 46 pp 123ndash133 2015

[5] S Safinia Z Al-Hinai H A Yahia and M F AbushammalaldquoSustainable construction in sultanate of oman factors effectingmaterials utilizationrdquo Procedia Engineering vol 196 pp 980ndash987 2017

[6] N B Dang S Momtaz K Zimmerman P Thi and H NhungldquoEffectiveness of formal institutions in managing marine fish-eries for sustainable fisheries development A case study of acoastal commune inVietnamrdquoOcean CoastalManagement vol137 pp 175ndash184 2017

[7] A Fleming R M Wise H Hansen and L Sams ldquoThesustainable development goals A case studyrdquoMarine Policy vol86 pp 94ndash103 2017

[8] S Hernandez Aguado I Segado Segado and T J PitcherldquoTowards sustainable fisheries A multi-criteria participatoryapproach to assessing indicators of sustainable fishing commu-nities A case study fromCartagena (Spain)rdquoMarine Policy vol65 pp 97ndash106 2016

[9] I B M Kosamu ldquoConditions for sustainability of small-scalefisheries in developing countriesrdquo Fisheries Research vol 161pp 365ndash373 2015

[10] A Lucchetti S E A Kholeif H H Mahmoud and ENotti ldquoTowards sustainable fisheries management in emergingmarkets An overview of properties gaps and opportunities inEgyptrdquoMarine Policy vol 72 pp 1ndash10 2016

[11] M Rossetto I Bitetto M T Spedicato et al ldquoMulti-criteriadecision-making for fisheries management A case study ofMediterranean demersal fisheriesrdquo Marine Policy vol 53 pp83ndash93 2015


[12] S S Erzurumlu and Y O Erzurumlu ldquoSustainable miningdevelopment with community using design thinking andmulti-criteria decision analysisrdquo Resources Policy vol 46 pp 6ndash142015

[13] S Kusi-Sarpong C Bai J Sarkis and X Wang ldquoGreen supplychain practices evaluation in the mining industry using a jointrough sets and fuzzy TOPSIS methodologyrdquo Resources Policyvol 46 pp 86ndash100 2015

[14] S Luthra D Garg and A Haleem ldquoAn analysis of interactionsamong critical success factors to implement green supply chainmanagement towards sustainability An Indian perspectiverdquoResources Policy vol 46 pp 37ndash50 2015

[15] B S Pimentel E S Gonzalez and G N O Barbosa ldquoDecision-supportmodels for sustainablemining networks Fundamentalsand challengesrdquo Journal of Cleaner Production vol 112 pp2145ndash2157 2016

[16] L Shen K Muduli and A Barve ldquoDeveloping a sustainabledevelopment framework in the context of mining industriesAHP approachrdquo Resources Policy vol 46 pp 15ndash26 2015

[17] R Sivakumar D Kannan and P Murugesan ldquoGreen vendorevaluation and selection using AHP and Taguchi loss functionsin production outsourcing inmining industryrdquoResources Policyvol 46 pp 64ndash75 2015

[18] M Abbasi and F Nilsson ldquoDeveloping environmentally sus-tainable logisticsrdquo Transportation Research Part D Transportand Environment vol 46 pp 273ndash283 2016

[19] V de Almeida Guimaraes and I C Leal Junior ldquoPerformanceassessment and evaluation method for passenger transporta-tion a step toward sustainabilityrdquo Journal of Cleaner Productionvol 142 pp 297ndash307 2017

[20] YHuizheM Lihua and S Fangfang ldquoEvaluation of sustainabledevelopment ability for logistics enterprises based on unascer-tained measurerdquo Procedia Engineering vol 15 pp 4757ndash47622011

[21] M Jedlinski ldquoThe position of green logistics in sustainabledevelopment of a smart green cityrdquo Procedia - Social andBehavioral Sciences vol 151 pp 102ndash111 2014

[22] A S Santos and S K Ribeiro ldquoThe use of sustainabilityindicators in urban passenger transport during the decision-making process The case of Rio de Janeiro Brazilrdquo CurrentOpinion in Environmental Sustainability vol 5 no 2 pp 251ndash260 2013

[23] O Seroka-Stolka ldquoThe development of green logistics forimplementation sustainable development strategy in compa-niesrdquo Procedia - Social and Behavioral Sciences vol 151 pp 302ndash309 2014

[24] S Zailani K GovindanM IranmaneshM R Shaharudin andY Sia Chong ldquoGreen innovation adoption in automotive supplychain The Malaysian caserdquo Journal of Cleaner Production vol108 pp 1115ndash1122 2015

[25] S H Cheraghi M Dadashzadeh and M Subramanian ldquoCriti-cal success factors for supplier selection an updaterdquo Journal ofApplied Business Research (JABR) vol 20 no 2 pp 91ndash108 2011

[26] V Baskaran S Nachiappan and S Rahman ldquoIndian textilesuppliersrsquo sustainability evaluation using the grey approachrdquoInternational Journal of Production Economics vol 135 no 2pp 647ndash658 2012

[27] P M Simpson J A Siguaw and S C White ldquoMeasuring theperformance of suppliers an analysis of evaluation processesrdquoJournal of Supply Chain Management vol 38 no 1 pp 29ndash412002

[28] W Ho X Xu and P K Dey ldquoMulti-criteria decision makingapproaches for supplier evaluation and selection a literaturereviewrdquo European Journal of Operational Research vol 202 no1 pp 16ndash24 2010

[29] G Buyukozkan and G Cifci ldquoA novel hybrid MCDM approachbased on fuzzy DEMATEL fuzzy ANP and fuzzy TOPSIS toevaluate green suppliersrdquo Expert Systems with Applications vol39 no 3 pp 3000ndash3011 2012

[30] G W Dickson ldquoAn analysis of vendor selection systems anddecisionsrdquo Journal of Purchasing vol 2 no 1 pp 5ndash17 1966

[31] D Kannan A B L D S Jabbour C Jose and C J C JabbourldquoSelecting green suppliers based on GSCM practices usingfuzzy TOPSIS applied to a Brazilian electronics companyrdquoEuropean Journal of Operational Research vol 233 no 2 pp432ndash447 2014

[32] A H I Lee H Kang C F Hsu and H Hung ldquoA green supplierselection model for high-tech industryrdquo Expert Systems withApplications vol 36 no 4 pp 7917ndash7927 2009

[33] R J Kuo Y C Wang and F C Tien ldquoIntegration of artificialneural network and MADA methods for green supplier selec-tionrdquo Journal of Cleaner Production vol 18 no 12 pp 1161ndash11702010

[34] S Luthra K Govindan D Kannan S K Mangla and CP Garg ldquoAn integrated framework for sustainable supplierselection and evaluation in supply chainsrdquo Journal of CleanerProduction vol 140 pp 1686ndash1698 2017

[35] M R Galankashi A Chegeni A Soleimanynanadegany etal ldquoPrioritizing green supplier selection criteria using fuzzyanalytical network processrdquo Procedia CIRP vol 26 pp 689ndash694 2015

[36] K Govindan S Rajendran J Sarkis and P Murugesan ldquoMulticriteria decision making approaches for green supplier eval-uation and selection a literature reviewrdquo Journal of CleanerProduction vol 98 pp 66ndash83 2015

[37] D Kannan K Govindan and S Rajendran ldquoFuzzy axiomaticdesign approach based green supplier selection a case studyfrom Singaporerdquo Journal of Cleaner Production vol 96 pp 194ndash208 2015

[38] G Noci ldquoDesigning green vendor rating systems for theassessment of a suppliers environmental performancerdquo Euro-pean Journal of Purchasing Supply Management vol 3 no 2 pp103ndash114 1997

[39] R Handfield S V Walton R Sroufe and S A MelnykldquoApplying environmental criteria to supplier assessment astudy in the application of the Analytical Hierarchy ProcessrdquoEuropean Journal of Operational Research vol 141 no 1 pp 70ndash87 2002

[40] P Humphreys R McIvor and F Chan ldquoUsing case-basedreasoning to evaluate supplier environmental managementperformancerdquo Expert Systems with Applications vol 25 no 2pp 141ndash153 2003

[41] G Buyukozkan and G Cifci ldquoA novel fuzzy multi-criteriadecision framework for sustainable supplier selection withincomplete informationrdquo Computers in Industry vol 62 no 2pp 164ndash174 2011

[42] D Kannan R Khodaverdi L Olfat A Jafarian and A DiabatldquoIntegrated fuzzy multi criteria decision making method andmulti-objective programming approach for supplier selectionand order allocation in a green supply chainrdquo Journal of CleanerProduction vol 47 pp 355ndash367 2013

[43] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network process


and improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[44] R Rostamzadeh K Govindan A Esmaeili and M SabaghildquoApplication of fuzzy VIKOR for evaluation of green supplychain management practicesrdquo Ecological Indicators vol 49 pp188ndash203 2014

[45] A Awasthi and G Kannan ldquoGreen supplier developmentprogram selection usingNGTandVIKORunder fuzzy environ-mentrdquo Computers amp Industrial Engineering vol 91 pp 100ndash1082016

[46] OUygun andADede ldquoPerformance evaluation of green supplychainmanagement using integrated fuzzymulti-attributes deci-sion making techniquesrdquo Computers amp Industrial Engineeringvol 102 pp 502ndash511 2016

[47] Z Guo H Liu D Zhang and J Yang ldquoGreen supplierevaluation and selection in apparel manufacturing using a fuzzymulti-attributes decision-making approachrdquo Sustainability vol9 no 4 pp 1ndash13 2017

[48] K-Q Wang H-C Liu L Liu and J Huang ldquoGreen supplierevaluation and selection using cloud model theory and theQUALIFLEX methodrdquo Sustainability vol 9 no 5 p 688 2017

[49] F Vahidi S A Torabi and M J Ramezankhani ldquoSustainablesupplier selection and order allocation under operational anddisruption risksrdquo Journal of Cleaner Production vol 174 pp1351ndash1365 2018

[50] F Yu Y Yang and D Chang ldquoCarbon footprint based greensupplier selection under dynamic environmentrdquo Journal ofCleaner Production vol 170 pp 880ndash889 2018

[51] S Vachon and R D Klassen ldquoEnvironmental management andmanufacturing performance The role of collaboration in thesupply chainrdquo International Journal of Production Economicsvol 111 no 2 pp 299ndash315 2008

[52] Q Zhu and J Sarkis ldquoAn inter-sectoral comparison of greensupply chain management in China drivers and practicesrdquoJournal of Cleaner Production vol 14 no 5 pp 472ndash486 2006

[53] S K Srivastava ldquoGreen supply-chain management a state-of-the-art literature reviewrdquo International Journal of ManagementReviews vol 9 no 1 pp 53ndash80 2007

[54] M E Gonzalez G Quesada and C A M Monge ldquoDeter-mining the importance of the supplier selection process inmanufacturing a case studyrdquo International Journal of PhysicalDistribution ampamp Logistics Management vol 34 no 6 pp492ndash504 2004

[55] A Amindoust S Ahmed A Saghafinia and A BahreininejadldquoSustainable supplier selection a ranking model based on fuzzyinference systemrdquo Applied Soft Computing vol 12 no 6 pp1668ndash1677 2012

[56] M Zamani A Rabbani A Yazdani-Chamzini and Z TurskisldquoAn integrated model for extending brand based on fuzzyARAS and ANP methodsrdquo Journal of Business Economics andManagement vol 15 no 3 pp 403ndash423 2014

[57] A Balezentis T Balezentis and W K M Brauers ldquoPersonnelselection based on computing with words and fuzzy MULTI-MOORArdquo Expert Systems with Applications vol 39 no 9 pp7961ndash7967 2012

[58] M Yazdani A Alidoosti and E K Zavadskas ldquoRisk analysis ofcritical infrastructures using fuzzy coprasrdquo Economic Research-Ekonomska Istrazivanja vol 24 no 4 pp 27ndash40 2015

[59] A T Gumus A Yesim Yayla E Celik and A Yildiz ldquoA com-bined fuzzy-AHP and fuzzy-GRA methodology for hydrogenenergy storage method selection in Turkeyrdquo Energies vol 6 no6 pp 3017ndash3032 2013

[60] H M W Chen S Y Chou Q D Luu and T H K Yu ldquoAfuzzy MCDM approach for green supplier selection from theeconomic and environmental aspectsrdquo Mathematical Problemsin Engineering vol 2016 Article ID 8097386 10 pages 2016

[61] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multicriteriadecision making approach for green supplier selection in low-carbon supply chainrdquo Mathematical Problems in Engineeringvol 2017 Article ID 9653261 9 pages 2017

[62] M Yucesan S Mete F Serin E Celik and M Gul ldquoAn inte-grated best-worst and interval type-2 fuzzy topsis methodologyfor green supplier selectionrdquo Mathematics vol 7 no 2 p 1822019

[63] K Maniya and M G A Bhatt ldquoA selection of material using anovel type decision-makingmethod Preference selection indexmethodrdquoMaterials amp Design vol 31 no 4 pp 1785ndash1789 2010

[64] D S Yakowitz L J Lane and F Szidarovszky ldquoMulti-attributedecision making dominance with respect to an importanceorder of the attributesrdquo Applied Mathematics and Computationvol 54 no 2-3 pp 167ndash181 1993

[65] V Penades-Pla T Garcıa-Segura J Martı and V Yepes ldquoAreview of multi-criteria decision-making methods applied tothe sustainable bridge designrdquo Sustainability vol 8 no 12 p1295 2016

[66] E K Zavadskas Z Nunic Z Stjepanovic and O PrentkovskisldquoA novel rough range of value method (R-ROV) for selectingautomatically guided vehicles (AGVs)rdquo Studies in Informaticsand Control vol 27 no 4 pp 385ndash394 2018

[67] A N Gani and S N M Assarudeen ldquoA new operation ontriangular fuzzy number for solving fuzzy linear programmingproblemrdquo Applied Mathematical Sciences vol 6 no 11 pp 525ndash532 2012

[68] P J V Laarhoven and W Pedrycz ldquoA fuzzy extension of saatyrsquospriority theoryrdquo Fuzzy Sets and Systems vol 11 no 1-3 pp 229ndash241 1983

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Table 1 The most common used economic attributes in supplier selection

Quality Financial PerformanceDelivery (Time) Management and OrganizationPrice Production Facilities and CapacityFlexibility ReliabilityTechnical Capability Long-term RelationshipSources [25ndash37]

For this purpose this paper proposes determining thegreen attributes for the selection of supplier and then devel-oping a model for assessing and ordering of green suppliersbased on determined attributes Three contributions havebeen made into the literature by this paper The first is topropose a novel model which is fuzzy extension of rangeof value (FROV) to literature Generally fuzzy extension ofpreference selection index (FPSI) has not been applied toacquire attribute weights so the second is to utilize FPSI toidentify the weights of attributes The third is to develop anovel fuzzy multiattribute decision-making (MADM) modelconsisting of FPSI and FROV to address supplier selectionproblem for a Turkish textile company

The rest of the paper is organized as follows After theintroduction the attributes used for selecting green supplierin the literature are reviewed in Section 2 Then the novelmodel is explained in detail in Section 3 In Section 4the results are presented and the results of FROV arecompared with the results of other fuzzy MADM which arefuzzy additive ratio assessment (ARAS) [56] fuzzy multipleobjective optimization on the basis of ratio analysis plus fullmultiplicative form (MULTIMOORA) [57] fuzzy complexproportional assessment (COPRAS) [58] and fuzzy greyrelational analysis (GRA) [59] In Section 5 a sensitivityanalysis is done in order to observe the changing of the resultswith respect to the changing of attribute weights In Section 6a brief conclusion is presented

2 Literature Review

In the literature review section attributes utilized for greensupplier selection in the literature have been reviewed todetermine which attributes to be used in the model (Sec-tion 3) There are three groups of attributes in the literatureused for green supplier selection economic environmentaland social Environmental and social attributes are addressedas green attributes in this section

21 Economic Attributes Economic attributes have beenused commonly for a long time in supplier selection beforesustainability introduced to supply chain management [25]The economic attributes mostly used for supplier selectionwere summarized in Table 1

Due to the profit maximization objectives of firms priceattribute was once the most popular economic attribute usedin supplier selection [26 27] However it was shown thatprice attribute alone is insufficient for supplier selectionproblems in the literature review conducted by Ho et al [28]The review presented that quality delivery management

technology relationship and flexibility attributes are also sig-nificant in supplier selection besides price attribute Financialperformance attribute is deemed significant by Buyukozkanand Cifci [29] and Dickson [30] as it shows the stability andthus the continuity of supplier firms Dickson [30] presentedthe importance of production capacity in addition to theattributes mentioned above Kannan et al [31] indicated thatreliability attribute is among most common used traditionalattributes in the literature

As it is seen in the literature economic attributes arethe main focus for traditional supplier selection Howeverrecent changes in the economy and politics such as increasingcompetition and foreign trade consumers and governmentsgiving more importance to sustainability therefore requiredenvironmental and social attributes to be included in supplierselection

22 Green Attributes Several studies in the literatureaddressed the green attributes (social and environmental) insupplier selection problems Table 2 summarizes the greenattributes used in the literature

Noci [38] presented a supplier selection model basedon environmental performance of suppliers It was claimedthat increasing concerns about environmental performanceof corporates will lead the corporates to choose suppliersbased on an environmental viewpoint Handfield et al [39]presented an analytic hierarchy process (AHP) based supplierselection model to be used in the selection of suppliersbased on environmental responsibility attribute Humphreyset al [40] introduced a supplier selection decision-makingmodel by using Knowledge-Based System (KBS) which usedqualitative and quantitative environmental attributes

Lee et al [32] developed an integrated model includ-ing fuzzy AHP and Delphi methods to choose the mostappropriate green suppliers for corporations Kuo et al[33] created green supplier selection model by integratingthe artificial neural network (ANN) the data envelopmentanalysis (DEA) and analytic network process (ANP)

Buyukozkan and Cifci [41] conducted a study to eval-uate the sustainability of suppliers with ANP Kannan etal [42] selected suppliers based on economic and envi-ronmental attributes in their model integrating fuzzy AHPfuzzy technique for order preference by similarity to idealsolution (TOPSIS) multiobjective linear programming andfuzzy logic Hashemi et al [43] suggested a comprehensivegreen supplier selection model by using ANP the traditionalGRA and both economic and environmental attributesRostamzadeh et al [44] presented a model for evaluatinggreen suppliers based on quantitative data by using fuzzy sets










3 Methodology







119889119894119895 = 1119870119870sum119896=1

119889119894119895119896 (1)




119894119895 = 119889119894119895max (119889119894119895) (2)

119894119895 = min (119889119894119895)119889119894119895 (3)


119894119895 = 1119898119898sum119894=1

119894119895 (4)


119875119881119895 = 119898sum119894=1

(119894119895 minus 119894119895)2 (5)



(6)

119908119895 = 119895sum119899119895=1 119895 (7)









max (119889119906119894119895) minusmin (119889119897119894119895))

(9)




max (119889119906119894119895) minusmin (119889119897119894119895))

(10)



minus119894 = 119891sum119894=1

119904119894119895119908119895 (11)

+119894 = 119898sum119894=119891+1

119904119894119895119908119895 (12)


119894 = minus119894 + +1198942 (13)


119906119894 = 119906119897119894 + 119906119898119894 + 1199061199061198943 (14)


4 Application


























PVj (000900150064) (001200250051) (002800730158)j (093609850991) (094909750988) (084209270972)wj (011201320156) (011401300156) (010101240153)119908lowast119895 (0109 0129 0152) (0111 0127 0152) (0099 0121 0149)


PVj (010101250126) (010601270130) (005900960185)j (087408750899) (087008730894) (081509040941)wj (010501170142) (010501160141) (009801210148)119908lowast119895 (0102 0114 0139) (0102 0113 0138) (0096 0118 0144)


PVj (014502450507) (012904221172) (008403801385)j (049307550855) (017205780871) (038506200916)wj (005901010135) (002100770137) (004600830144)119908lowast119895 (0058 0099 0132) (0020 0075 0134) (0045 0081 0141)









012345678

1 2 3 4 5

Rank

ing




















6 Conclusion












Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018

















3 Methodology







119889119894119895 = 1119870119870sum119896=1

119889119894119895119896 (1)




119894119895 = 119889119894119895max (119889119894119895) (2)

119894119895 = min (119889119894119895)119889119894119895 (3)


119894119895 = 1119898119898sum119894=1

119894119895 (4)


119875119881119895 = 119898sum119894=1

(119894119895 minus 119894119895)2 (5)



(6)

119908119895 = 119895sum119899119895=1 119895 (7)









max (119889119906119894119895) minusmin (119889119897119894119895))

(9)




max (119889119906119894119895) minusmin (119889119897119894119895))

(10)



minus119894 = 119891sum119894=1

119904119894119895119908119895 (11)

+119894 = 119898sum119894=119891+1

119904119894119895119908119895 (12)


119894 = minus119894 + +1198942 (13)


119906119894 = 119906119897119894 + 119906119898119894 + 1199061199061198943 (14)


4 Application


























PVj (000900150064) (001200250051) (002800730158)j (093609850991) (094909750988) (084209270972)wj (011201320156) (011401300156) (010101240153)119908lowast119895 (0109 0129 0152) (0111 0127 0152) (0099 0121 0149)


PVj (010101250126) (010601270130) (005900960185)j (087408750899) (087008730894) (081509040941)wj (010501170142) (010501160141) (009801210148)119908lowast119895 (0102 0114 0139) (0102 0113 0138) (0096 0118 0144)


PVj (014502450507) (012904221172) (008403801385)j (049307550855) (017205780871) (038506200916)wj (005901010135) (002100770137) (004600830144)119908lowast119895 (0058 0099 0132) (0020 0075 0134) (0045 0081 0141)









012345678

1 2 3 4 5

Rank

ing




















6 Conclusion












Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018










119894119895 = 119889119894119895max (119889119894119895) (2)

119894119895 = min (119889119894119895)119889119894119895 (3)


119894119895 = 1119898119898sum119894=1

119894119895 (4)


119875119881119895 = 119898sum119894=1

(119894119895 minus 119894119895)2 (5)



(6)

119908119895 = 119895sum119899119895=1 119895 (7)









max (119889119906119894119895) minusmin (119889119897119894119895))

(9)




max (119889119906119894119895) minusmin (119889119897119894119895))

(10)



minus119894 = 119891sum119894=1

119904119894119895119908119895 (11)

+119894 = 119898sum119894=119891+1

119904119894119895119908119895 (12)


119894 = minus119894 + +1198942 (13)


119906119894 = 119906119897119894 + 119906119898119894 + 1199061199061198943 (14)


4 Application


























PVj (000900150064) (001200250051) (002800730158)j (093609850991) (094909750988) (084209270972)wj (011201320156) (011401300156) (010101240153)119908lowast119895 (0109 0129 0152) (0111 0127 0152) (0099 0121 0149)


PVj (010101250126) (010601270130) (005900960185)j (087408750899) (087008730894) (081509040941)wj (010501170142) (010501160141) (009801210148)119908lowast119895 (0102 0114 0139) (0102 0113 0138) (0096 0118 0144)


PVj (014502450507) (012904221172) (008403801385)j (049307550855) (017205780871) (038506200916)wj (005901010135) (002100770137) (004600830144)119908lowast119895 (0058 0099 0132) (0020 0075 0134) (0045 0081 0141)









012345678

1 2 3 4 5

Rank

ing




















6 Conclusion












Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018
































PVj (000900150064) (001200250051) (002800730158)j (093609850991) (094909750988) (084209270972)wj (011201320156) (011401300156) (010101240153)119908lowast119895 (0109 0129 0152) (0111 0127 0152) (0099 0121 0149)


PVj (010101250126) (010601270130) (005900960185)j (087408750899) (087008730894) (081509040941)wj (010501170142) (010501160141) (009801210148)119908lowast119895 (0102 0114 0139) (0102 0113 0138) (0096 0118 0144)


PVj (014502450507) (012904221172) (008403801385)j (049307550855) (017205780871) (038506200916)wj (005901010135) (002100770137) (004600830144)119908lowast119895 (0058 0099 0132) (0020 0075 0134) (0045 0081 0141)









012345678

1 2 3 4 5

Rank

ing




















6 Conclusion












Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018


















PVj (000900150064) (001200250051) (002800730158)j (093609850991) (094909750988) (084209270972)wj (011201320156) (011401300156) (010101240153)119908lowast119895 (0109 0129 0152) (0111 0127 0152) (0099 0121 0149)


PVj (010101250126) (010601270130) (005900960185)j (087408750899) (087008730894) (081509040941)wj (010501170142) (010501160141) (009801210148)119908lowast119895 (0102 0114 0139) (0102 0113 0138) (0096 0118 0144)


PVj (014502450507) (012904221172) (008403801385)j (049307550855) (017205780871) (038506200916)wj (005901010135) (002100770137) (004600830144)119908lowast119895 (0058 0099 0132) (0020 0075 0134) (0045 0081 0141)









012345678

1 2 3 4 5

Rank

ing




















6 Conclusion












Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018
















012345678

1 2 3 4 5

Rank

ing




















6 Conclusion












Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018




















6 Conclusion












Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018

















Data Availability




References















































































Journal of












Journal of







Volume 2018






Volume 2018











































































Journal of












Journal of







Volume 2018






Volume 2018










































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

An Application of Fuzzy Integrated Model in Green Supplier