resilient supplier selection based on fuzzy bwm...

Research ArticleResilient Supplier Selection Based on Fuzzy BWM andGMo-RTOPSIS under Supply Chain Environment

Jiawu Gan 1 Shuqi Zhong1 Sen Liu 2 and Dan Yang1

1 International Business School Yunnan University of Finance and Economics Kunming 650221 China2School of Logistics Yunnan University of Finance and Economics Kunming 650221 China

Correspondence should be addressed to Jiawu Gan andy ganynufeeducn

Received 28 January 2019 Accepted 12 March 2019 Published 7 April 2019

Academic Editor Paolo Renna

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

Resilient suppliers can reduce supply chain risk effectively avoid supply chain disruption and bring profits to enterprisesHoweverthere is no united measuring index system to evaluate the resilient supplier under supply chain environment and the assessmentlanguage sets are usually crisp values Therefore in order to fill the research gap this paper proposes a hybrid method whichcombines triangular fuzzy number the best-worst method (BWM) and the modular TOPSIS in random environments for groupdecision-making (GMo-RTOPSIS) to solve the above problem Firstly the weight of decision-maker is calculated by using fuzzyBWM which can deal with triangular fuzzy numbers Secondly triangular fuzzy number is introduced into GMo-RTOPSIS andcombined with fuzzy BWM alternatives are sorted to select the best resilient supply chain partner Finally the feasibility anduniversality of this method are proved by illustrative examples

1 Introduction

As a result of globalization supply chains are confrontedwith natural disastersman-made disasters and technologicalthreats at any time [1] These disasters will cause supplychain interruption and shortage of raw materials such asfloods and other natural disasters and the gradual increaseof timber costs these disasters lead to fluctuations in rawmaterials quality and interruption of delivery dates resultingin supply chain fluctuations [2 3] Man-madetechnologicaldisasters such as fires traffic accidents technology leaks andterrorist attacks can also lead to supply chain disruption andincreasing supply chain resilience can alleviate the disruptionproblem Since suppliers are the main external risks of supplychain how to choose resilient suppliers becomes an effectiveway to avoid supply chain interruption [4 5]

Holling [6] first proposed the concept of resilience andpointed out that resilience is the ability to absorb change Sub-sequently Scholar believes that elasticity should be defined asthe ability of enterprises to deal with inevitable disasters link-ing elasticity with absorptivity and resilience Yang and Xu[7] preferred to define resilience as the ability of an enterprise

to respond to natural disasters the resilience can be assessedby the rate of recovery Through literature review resilienceis a necessary factor in the selection of suppliers and howto choose more resilient suppliers has become the researchobject of scholars Sustainable development of enterprises isrelated to how to deal with disruption situations and thechoice of resilient suppliers is an important factor in dealingwith interruption situation properly [8] Choosing supplierswith good quality can enhance the resilience of supply chainand reduce the overall risk of supply chain [5] At present formost scholars from the perspective of improving supply chainto improve resilience [9ndash12] research has become mature Afew scholars have begun to evaluate resilient suppliers fromthe perspective of the capabilities they need before when andafter disruption which ismore scientific As a relatively blankresearch area this paper chooses the absorptive capacityadaptive capacity and restorative capacity described as theselection criteria of resilient suppliers

Rajesh and Ravi [4] uses grey relational analysis tocalculate the grey possibility value and select resilient sup-pliers Valipour Parkouhi and Safaei Ghadikolaei [5] choseprice fluctuation vulnerability supplier capacity limit and

HindawiDiscrete Dynamics in Nature and SocietyVolume 2019 Article ID 2456260 14 pageshttpsdoiorg10115520192456260

2 Discrete Dynamics in Nature and Society

visibility as indicators and determined supplierrsquos elasticitylevel by combining fuzzy analysis network process and greyVIKOR Haldar et al [13] combined fuzzy TOPSIS and fuzzyweight method to select resilient suppliers which can reducethe vulnerability of supply chain system Pramanik et al [14]uses AHP-TOPSIS-QFD to measure supplier performance inorder to select a resilient supplier

However through literature review we find that the sup-plier selection in resilient supply chain still has limitationsFirstly few studies have been conducted on the selection ofresilient suppliers Secondly many multiattribute decision-making methods strongly restrict the freedom of decision-makers to use the type of information which greatly reducesthe personal opinions of relevant decision-makersThirdly inmost studies decision-makers have to reach an agreement oncriteria which is difficult to achieve Fourthly crisp numbercannot accurately describe the decision-makerrsquos evaluation ofalternatives Therefore in order to fill the research gap weproposed a method combining fuzzy BWM and improvedTOPSIS to determine the weight of decision-makers and rankthe alternatives for supplier selection in resilient supply chainFinally the practicability of this method is proved by theillustrative example

The structure of this paper is divided into seven partsThe second section is literature review the third sectionproposes the evaluation criteria of resilient supplier selectionunder supply chain environment Section four introducesthe preliminaries including some definitions The proposedmethod is proposed in the fifth section Section six introducesthe illustrative example Finally the conclusions are presentedin section seven

2 Literature Review

Some early researchers defined resilience as the ability of asystem to recover from disruption [15 16] In the definitionof resilience by scholars Allenby and Fink [17] and Pregenzer[18] the ability of the system to maintain function in thedisaster is emphasized Haimes [19] proposed the definitionof resilience refers to the ability of withstand the disruptionand recovery with reasonable time and costs After thatscholars state that the key to enhancing resilience is that thesupply chain process should bemanaged and put forward theprinciple of building a resilient supply chain [20 21] Hol-comb and Ponomarov [22] proposed that logistics capacity isrelated to resilience coordination and integration capabilitiescan enhance the ability to confront disruption Maklan andJuttner [23] argued that risk management and knowledgemanagement have an impact on resilience Hosseini et al[24] proposed the method of literature classification andthrough literature review studied the application domain ofresilience and identified four areas of resilient applicationorganizational domain social domain economic domainand engineering domain Papadopoulos et al [11] emphasizedthe role of swift trust public-private partnerships and qualityof information sharing in promoting supply chain resilience

Supplier selection is an important issue in the resilientsupply chain and daily operation of enterprises It is regarded

as a strategic choice of enterprises [25] and also a difficultand complex process [26] In the 1990s scholars beganto study the selection of business suppliers Subsequentlyscholars subdivided the selection of suppliers such as thechoice of sustainable suppliers and resilient suppliers andthe criteria considered in the selection process changedaccordingly However scholars have not reached a consensuson the selection criteria of resilient suppliers Christopherand Peck [20] discussed the upstream inventory and supplyconditions on impact of supply chain resilience Rajesh andRavi [4] considered that when choosing resilient suppliersthe key factors that should be considered include vul-nerability collaboration risk awareness and supply chaincontinuity management Baek et al [27] argued that thedriving factor of resilient supply chain is flexibility whileTamvakis et al [28] emphasize the role of transportationVugrin et al [29] define resilience from the perspectives ofpredisruption prevention and postdisruption recovery andconsidered that resilience includes absorptive adaptive andrestorative capacities Scholar Hosseini extends the contentof resilience subdivides the criteria of absorptive adaptiveand restorative capacities in different application domainquantifies the resilience of inland waterway ports and sulfuricacid manufacturer with Bayesian network and studies theselection of resilient suppliers [30ndash32]

Supplier selection essentially is a multiattribute decision-making problem and there are many methods to deal withsuch problems in the field of supply chain for exampleTechnique for Order Preference by Similarity to Ideal Solu-tion (TOPSIS) and improved TOPSIS [25 33ndash35] AnalyticHierarchy Process (AHP) and its extension [25 26 36] ANP[37]Data Envelopment Analysis (DEA) and its improvement[38ndash40] VIKOR [5 41 42] and best-worst multicriteriadecision-making method (BWM) [43 44] BWM has onlybeen proposed in recent years the relevant research isrelatively blank which is a direction of great research value

BWM is proposed by Rezaei [45] compared with AHPBWM needs less data for comparison and the final resultis consistent with AHP [46] BWM greatly reduces thecomplexity of calculation And throughmore consistent com-parisons the final result will be more credible However thetraditional BWM cannot determine the weight in uncertainenvironment [47] so scholars have improved BWM andfuzzy BWM has been developed [48ndash50] BWM based ontriangular fuzzy numbers is one of them BWM has beenused in many areas and has solved some practical problemssuch as evaluating the service quality of baggage handlingsystems [51] cloud service selection [52] identifying successfactors in eXtensible Business Reporting Language (XBRL)[53] performance evaluation and ranking of airports [54]identifying the research and development (RampD) of enter-prises [55] assessment of the technologies for the treatmentof urban sewage sludge [56] etc

As a common method TOPSIS is proposed by Hwangand Yoon [57] The principle of TOPSIS is to make the idealsolution as close to positive-ideal solution (PIS) as possibleand as far away fromnegative-ideal solution (NIS) as possibleHowever the traditional TOPSIS still has some limitations Itcan only deal with the information of a single decision-maker

Discrete Dynamics in Nature and Society 3

and can only have crisp numbers in the decision matrixIn order to expand the research field of TOPSIS scholarshave proposed improved TOPSIS methods such as TOPSISwhich can deal with interval numbers [58ndash60] TOPSIScontaining fuzzy information [61ndash63] combination of TOP-SIS and intuitionistic fuzzy information [64] and TOPSISmethod which can process information of multiple decision-makers [62 64ndash67] One of the most important methodGMo-RTOPSIS proposed by Lourenzutti and Krohling [68]has been applied to a wider range of research areas Ithas the following advantages (1) It can process decisioninformation in dynamic environment (2) Unlike traditionalTOPSIS GMo-RTOPSIS divides decision matrix into smallermodules each module can use different information typesand there is no need to unify the information types (3) Inaddition to crisp numbers it can handle random variables(4)Decision-makers need not discuss together to get a set ofcriteria each decision-maker can decide the criteria in thedecision matrix independently (5) Information of multipledecision-makers can be processed simultaneously

Literature review shows that there are still limitations inthe selection of resilient suppliers (1) Studies on supplierselection criteria focus more on cost raw material qualityscience technology and services Nowadays supply chainis in a changing environment resilient suppliers must havethe ability to cope with disruptions Responsiveness riskreduction geographical segregation and other capabilitiesshould be considered in the selection of resilient suppliers[1] Therefore how to use appropriate tools to select resilientsuppliers has become an important research object (2)The language of the decision-makers and its difficulty inaccurately describing lead to the deviation of the results ofweight calculation and alternatives ranking (3) When theareas of decision-makers are different the unified criteriaand weights of alternatives become unattainable Decision-makers have different evaluation criteria and weights onthe alternatives and the final results take into account thecomprehensiveness and scientificity of the alternatives

Therefore in order to fill the research gap this paperintroduces the selection of resilient suppliers in supply chaincombining triangular fuzzy number best-worst method(BWM) and the Modular TOPSIS in random environmentsfor group decision-making (GMo-RTOPSIS) Fuzzy BWMis introduced into multicriteria decision-making problemsto calculate decision-makersrsquo weights more accurately GMo-RTOPSIS is used to calculate the decision matrix given bydecision-makers independently and the suppliers of resilientsupply chain are ranked according to the decision-makersrsquoweight obtained by fuzzy BWM Finally an example is givento verify the effectiveness of the proposed method

The reason why we integrate fuzzy BWM with TOPSISis that the combination of the two methods makes theselection process simpler and the results more consistentand scientific The specific reasons are as follows (i) As thelatest MAGDMmethod BWMhas the advantages of simplercalculation process and more reliable weight distributionresults compared with other methods For example the AHPmethod has similar principles with BWM [45] but AHPuses pairwise comparison In the process of data comparison

it compares more times than BWM and involves fractionwhich increases the computational complexity At the sametime the BWM can remedy the inconsistency acquiredfrom pairwise comparisons [48] The procedure of BWMis much easier more precise and at less redundant dueto the fact that it does not involve secondary comparisonscompared with other methods [45] (ii) As a multiattributedecision-making method TOPSIS has better performancethan the other eight methods Zanakis et al [69] comparedeight MAGDM methods simple additive weighting (SAW)elimination (et) and choice translating reality (ELECTRE)multiplicative exponential weighting (MEW) TOPSIS andfour AHPs by a simulation study and discovered that TOP-SIS SAW and MEW performed best and ELECTRE wasthe worst Moreover Peng and Xiao [70] and Sun et al [71]pointed out that TOPSIS is a better decision-making skill forchoosing alternatives because of its clear and understandablelogic TOPSIS can also deal with qualitative and quantitativeproblems well [72] At the same time the improved modularTOPSIS has the ability to deal with multiattribute decision-making problems in dynamic environment it can alsodeal with decision-making information of multiple decision-makers and it does not require each decision-maker to havethe same criteria which greatly improves the freedom ofdecision process and the credibility of the final results [68]Besides due to triangular fuzzy number being able to solvethe problem of incomplete and inaccurate information inthe process of calculating weights and ranking alternativeswe integrate BWM GMo-RTOPSIS and triangular fuzzynumbers to solve the resilient supplier selection problemunder supply chain environment

3 The Criteria of Resilient Supplier Selectionunder Supply Chain Environment

Actively resilient planning of supplier can reduce the pos-sibility of disruption of supply chain system in the eventof disruptions [13] Torabi et al [8] argued that natural orman-made disasters would change the selection process andindicators of suppliers They distinguished the selection oftraditional suppliers from resilient suppliers and developed anewdecisionmodel for resilient supplier selectionThis paperconsiders the supplier selection criteria of resilient supplychain from the perspective of impact of naturalman-madedisasters

Vulnerability and recovery are two dimensions ofresilience and the main difference between the two dimen-sions is before and after the disruption [73ndash75] Vulnerabilityrefers to the systemrsquos resistant preparation and ability beforedisruption occurs Recovery refers to how the system adaptsto situations when disruption occurs and how to repair thesystem until normal operation Vulnerability and recoveryconstitute resilience which enables the resilient system tobetter respond to the whole process of disaster In absorptiveadaptive and restorative capacity proposed by Vugrin et al[29] the adaptive ability and restorative ability constituterecoverability [32] This paper refers to the criteria proposedby [76] for selection of resilient suppliersThe criteria include


Adaptive capacity

Surplus inventory

Restorative capacity

Absorptive capacity

Location separation

Reliability

Robustness

Interdependency

Rerouting

Reorganization

Restoration

Crite

ria o

f Res

ilien

t Sup

plie

r Sel

ectio

n

Figure 1 The criteria of resilient supplier selection under supply chain environment

the absorptive capacity adaptive capacity and restorativecapacity and their subcriteria for suppliers before duringand after disasters [76] The largest number of subprojectsincluded is absorptive capacity which means that suppliersmust invest a lot of money to improve absorptive capacitybefore disruptive events occur in order to absorb the damagecaused by shocks to the greatest extent when shocks occurRestorative capacity as an after-event maintenance requiressuppliers to spend enough manpower and capital to repairthe damage which belongs to the postevent repair so thiscontent is single and less important than absorptive capacityand adaptive capacity Figure 1 illustrates the criteria ofresilient supplier selection under supply chain environment[76]

31 Absorptive Capacity It is helpful for resilient supply chainmanagement [77] for suppliers to take appropriate measuresto prevent risks before they realize them With the change ofsupply chain environment the selection criteria of suppliersneed to be updated Hosseini and Barker [31] consideredsupplierrsquos absorptive capacity as an important capability andexamined the supply chainrsquos resilience adaptability to theenvironment and rebuilding ability from the perspective ofabsorbency Absorptive capacity mainly aims at improvingsuppliers before disruptive events so as to achieve its ownability to resist disruptions The evaluation of absorptivecapacity is mainly divided into the following five aspects

(i) Surplus Inventory Whether the supplier has surplusinventory is an important reflection of absorptive capacityThe presence of surplus inventory is the basic conditionfor manufacturers to quickly resume production and repairsupply chains in the event of naturalman-made disasters

Surplus inventory can make up for the production interrup-tion and the supply chain will not end immediately It allowsenterprises to have a competitive advantage among manysuppliers

(ii) Location Separation Location separation requires enter-prises to have separate production areas and spare productionareas When disaster occurs other production areas shouldquickly replenish their products to ensure that the supplychain is not interrupted

(iii) Interdependency Interdependency ismainly embodied inthe backup supplier contract The standby supplier refers tothe fact that the enterprise must select the standby supplierbefore the disruptive event occurs After the disruptions itcan establish a contract relationship with the standby supplierin time without causing the termination of production andquickly make up for the loss of production caused by thedisruptive event

(iv) Robustness Robustness indicates that supplierrsquos buildingin production area must have certain physical protectionWhen disaster occurs it can reduce the damage to equipmentand products and improving the resilience

(v) Reliability The more reliable the supplier is the lesslikely it will be impacted by man-made disasters Reliabilityrequires suppliers to provide reliable raw materials on timein their daily operations and to have confidence in theiraccounts Reliability is an important project of absorptivecapacity as a preparation in advance

32 Adaptive Capacity For supplier selection in resilientsupply chain not only should economic factors such as cost


and quality be considered but also whether suppliers canrespond to changes in the environment [78] adaptive capac-ity has become an important condition for evaluating supplierresilience In resilient supply chain flexibility has become animportant indicator to be considered in the selection processwhere flexibility includes that suppliers can quickly changethe original route and restructure and adapt to the changedsupply chain in the shortest possible time [79] Levalleand Nof [80] argued that team building is conducive toimproving resilience while emphasizing the important roleof cooperation supplier-competitor cooperation can preventsupply chain disruption under the necessary circumstance

Absorptive capacity emphasizes the ability of suppliersto withstand disruptions before they occur When disastersoccur absorptive capacity becomes ineffective and adaptivecapacity becomes the ability to assess how suppliers adapt tothe environment through their own changes The absorptivecapacity is embodied in the ability of supply chain reorga-nization which requires suppliers to have certain flexibilityto standardize and modularize products so that disruptiveevents can be quickly reorganized and repaired [81]

(i) Rerouting When disruptions occur suppliers can onlyadapt to changing environmental conditions by changingthemselves rerouting is an important aspect Rerouting refersto enterprises changing the usual mode of transport fastcombination of multiple modes of intermodal transportensures the normal transportation of goods and the operationof supply chain Changing the mode of transportation meansthat costs increase but it can prevent supply chain interrup-tion and improve the flexibility of enterprises in the supplychain

(ii) Reorganization When the organization is damagedsuppliers can quickly pool resources and acquire the ability toadapt to the new environment and rebuild the organizationand corporate culture In this case the organization cancooperate temporarily with its competitors to compensate forthe impact of other factors on the supply chain

33 Restorative Capacity Restorative capacity is the leastappealing of the three abilities that resilient suppliers shouldpossess because postdisaster reconstruction has little effecton disruption prevention and resistance suppliers only withpostdisaster reconstruction capability will increase the eco-nomic losses caused by disruptions

RC refers to the ability of suppliers to repair and quicklyrestore production after a disruptive event Technical supportfrom suppliers is an important manifestation of restorativecapacity [82]

(i) Restoration Themain indicators of restorations aremainlydivided into four aspects Firstly the enterprise has enoughmaintenance fund and maintenance equipment Then itneeds sufficient technical personnel to complete the mainte-nance process Finally the enterprise should have the abilityto quickly make up for the market vacancies caused by thedisruptions

4 Preliminaries

In this section we will introduce some mathematical con-cepts that may appear in the decision matrix of the GMo-RTOPSIS and provide some ways of normalization defuzzi-fication calculating distance and comparison size

41 Fuzzy Set Fuzzy set was proposed by Zadeh in 1965It converts the crisp value of the evaluation problem intoan interval on the axis Fuzzy set is used to deal with theproblem in uncertain environment We provide some basicconceptions of fuzzy set in the next section

Definition 1 (see [83]) Let 119886 be an fuzzy set in the universeof discourse X where 119886 = ⟨119909 120583119886(119909)⟩ 119909 isin 119883 120583119886 is amembership function 120583119886 119883 997888rarr [0 1] where 120583119886(119909) le 1 forall11990942 Triangular Fuzzy Set

Definition 2 let 119886 = (1198861 1198862 1198863) be a triangular fuzzy set(TrFN) where 1198861 lt 1198862 lt 1198863Definition 3 (see [84 85]) let 119886 = (1198861 1198862 1198863) be a TrFN thedefuzzified value of 119886 is as follows

119877 (119886) = 1198861 + 41198862 + 11988636 (1)

Definition 4 (see [86]) let 119886 = (1198861 1198862 1198863) and = (1198871 1198872 1198873)be two TrFN then the distance between them is given by

119889 (119886 ) = radic 133sum119894=1

(119886119894 minus 119887119894)2 (2)

Definition 5 When 119877(119886) gt 119877() we say 119886 is superior to Bycontraries 119886 is indifferent to if 119877(119886) = 119877()Definition 6 Let 119886119894119895 = (1198861119894119895 1198862119894119895 1198863119894119895) be a TrFN the normaliza-tion of 119886119894119895 is given by the following formula

119903119894119895 = ( 1198861119894119895max119894 1198863119894119895

1198862119894119895max119894 1198863119894119895

1198863119894119895max119894 1198863119894119895) 119894 = 1 sdot sdot sdot 119898 (3)

5 The Proposed Method

The research method proposed in this paper consists of threesteps in the preparation stage the reference comparisonmatrix of decision-makers is established and the comparisonresults are presented in the form of triangular fuzzy numbersThe second stage is aggregating using triangular fuzzy num-bers to improve BWM and determine the weight of decision-makers based on fuzzy BWM The third step is the selectionstage A new TOPSIS method namely GMo-RTOPSIS isintroduced to deal with the decision matrix provided bythe decision-makers By dealing with the decision matrixcontaining different information types a better scheme isobtained Figure 2 illustrates the conceptual framework of theproposed approach


Improvement of BWM

Calculation of decision-makers weight

Aggregation stage

Compute of closeness coefficients

Ranking of all alternatives

Selection stage

Establishment of reference comparisonmatrix of decision-makers

Integration of decision-maker matrix

Preparation stage

Fuzzy BWM

Triangular fuzzy set

GMo-RTOPSIS

Figure 2 The conceptual framework of the proposed approach

51 Collection of Decision Opinions and Establishing DecisionMatrices Let 119872 = 1 2 sdot sdot sdot 119898 119873 = 1 2 sdot sdot sdot 119899 119870 =1 2 sdot sdot sdot 119896 Let A = 1198601 1198602 sdot sdot sdot 119860119898(119898 ge 2) represent atotal of119898 alternatives and 119862 = 1198621 1198622 sdot sdot sdot 119862119899 denotes the 119899criterion ofA119908lowast = (119908lowast1 119908lowast2 sdot sdot sdot 119908lowast119896 ) is the weight of a groupof decision-makers wheresum119896119889=1119908119889 = 1 119889 isin 119870Y is a randomvector which effects A Let 119904(119889)119894119895 (Y(119889)) denote the ratings 119904119894119895 arerelated to random vector Y Notice in particular that 119904(119889)119894119895 and119904(119889)119897119895

must be the same type of information The evaluationinformation of 119860 119894 according to 119862119895 provided by decision-maker 119863119872(119889) is 119863119872(119889)(Y) = (119904(119889)119894119895 (Y(119889))) (119894 isin 119872 119895 isin 119873 119889 isin119870)

So each119863119872(119889)will provide its individual decisionmatrix119863119872(119889)(Y) including interval-numbers and triangular fuzzyset (TrFN) Moreover each matrix is allowed to considerdifferent criterion 119862119895DM(119889) (Y(119889))

=11986011198602119860119898

1198621 1198622 sdot sdot sdot 119862119899[[[[[[[[

119904(119889)11 (Y(119889))119904(119889)21 (Y(119889))119904(119889)1198981 (Y(119889))

119904(119889)12 (Y(119889))119904(119889)22 (Y(119889))119904(119889)1198982 (Y(119889))

sdot sdot sdotsdot sdot sdotdsdot sdot sdot

119904(119889)1119899 (Y(119889))119904(119889)2119899 (Y(119889))119904(119889)119898119899 (Y(119889))

]]]]]]]]

119889 = 1 sdot sdot sdot 119896

(4)

52 Weighting for Decision-Makers Based on Fuzzy BWMBest-worst method is proposed by Rezaei [45] which cansolve multiattribute decision-making problem The principleof this method is to replace secondary comparisons withreference comparisons thus reducing 1198992 comparison resultsto 2119899 minus 3 for simplifying the comparison process TraditionalBWM is only used to deal with crisp values After improve-ment by scholars [48] BWM can deal with multiattributedecision-making problems in fuzzy environment Compar-isons of criteria are described as linguistic labels where thelinguistic terms are expressed in triangular fuzzy numberswhich make the results much closer to the real ideas ofdecision-makers

The operation steps of fuzzy BWM are as followsFirstly compare the weights from 119896 decision-makers and

assume there are 119896 decision-makers 1198891 1198892 119889119896Secondly 119889119861 represents the best (most important) DM

under all criteria and the worst (least important) DM isexpressed as 119889119882

Thirdly determine the fuzzy preferences of the best overall the DMs by using the linguist labels in Table 1 [87]Similarly all the DMs over worst can be obtained by this step

AB = (1198861198611 1198861198612 sdot sdot sdot 119886119861119896) (5)

A119882 = (1198861119882 1198862119882 sdot sdot sdot 119886119896119882) (6)

Among them AB is vector of Best-to-Others and Others-to-Worst is labeled as A119882where 119886119861119895 = (ℎ119861119895 119896119861119895 119897119861119895) represents


Table 1 Transformation rules of linguistic variables of decision-makers

Linguistic terms Membership functionEquallyimportant(EI) (111)

Weaklyimportant(WI) (23 1 32)Fairlyimportant(FI) (32 2 52)Veryimportant(VI) (52 3 72)Absolutelyimportant(AI) (72 4 92)

TrFN preference of 119889119861 over decision-maker 119895 and 119886119894119882 =(ℎ119894119882 119896119894119882 119897119894119882) express TrFN preference of decision-maker 119894over 119889119882 Obviously 119886119861119861 = (1 1 1)

Fourthly we use fuzzy linguistic terms to indicate theweight of decision-maker 119895 as 119908119895 = (ℎ119908119895 119896119908119895 119897119908119895 ) in which119908119861 = (ℎ119908119861 119896119908119861 119897119908119861 ) (119908119882) reflects the weight of the most im-portant (least important) decision-makers

Fifth we get the optimal fuzzy weight (119908lowast1 119908lowast2 sdot sdot sdot 119908lowast119896 )through the following formula

min 120573119904119905 1003816100381610038161003816100381610038161003816100381610038161003816

119908119861119908119895 minus 1198861198611198951003816100381610038161003816100381610038161003816100381610038161003816 le 120573100381610038161003816100381610038161003816100381610038161003816

119908119895119908119882 minus 119886119895119882100381610038161003816100381610038161003816100381610038161003816 le 120573

119899sum119895=1

119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 sdot sdot sdot 119899

(7)

where 120573 = (ℎ120573 119896120573 119897120573) In order to transform the TrFNweight of DM to crisp weight we use the 119877 = (119908119895) = (ℎ119908119895 +4119896119908119895 + 119897119908119895 )6

The (7) can be transferred as [48]

min 120573lowast119904119905 10038161003816100381610038161003816100381610038161003816100381610038161003816

(ℎ119908119861 119896119908119861 119897119908119861 )(ℎ119908119895 119896119908119895 119897119908119895 ) minus (ℎ119861119895 119896119861119895 119897119861119895)10038161003816100381610038161003816100381610038161003816100381610038161003816 le (119901

lowast 119901lowast 119901lowast)10038161003816100381610038161003816100381610038161003816100381610038161003816(ℎ119908119895 119896119908119895 119897119908119895 )(ℎ119908119882 119896119908119882 119897119908119882) minus (ℎ119895119882 119896119895119882 119897119895119882)

10038161003816100381610038161003816100381610038161003816100381610038161003816 le (119901lowast 119901lowast 119901lowast)

119899sum119895=1

119877 (119908119895) = 1

ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 sdot sdot sdot 119899

(8)

where 120573lowast = (119901lowast 119901lowast 119901lowast) 119901lowast le ℎ120573 By solving (8) weobtained the weights of all the DMs (119908lowast1 119908lowast2 sdot sdot sdot 119908lowast119896 )53 GMo-RTOPSIS for Alternative Evaluation Hwang andYoon [88] proposed the TOPSIS theory which is a commonmethod to solve MAGDM problems in static environmentThe DMs need to unify the criteria in advance which limitthe freedom of decision-making The first step of TOPSISis to normalize the decision matrix and then aggregate theattribute weight into the matrix to get the normalized matrixwith weight The NIS and PIS 119903(119889)+minus119895 (Y) under each criterionare selected Then calculate the separation measures 119878+minus119894 (Y)for each alternative and the last step is to convert 119878+minus119894 (Y) intocloseness coefficients 119862119862119894 by formula the bigger the 119862119862119894 thebetter the alternative

After years of development traditional TOPSIS has beenunable to deal with more variable MAGDM problems Soscholars expand TOPSIS such as Modular-TOPSIS andTOPSIS with intuitionistic fuzzy set GMo-RTOPSIS is pro-posed by Lourenzutti and Krohling [68] As the extension ofTOPSIS GMo-RTOPSIS can deal with the independent deci-sion matrix provided by decision-makers without discussionIn the decision matrix each decision-maker can considerdifferent criteria use different information types for diversedecision criterion and also deal with the information typesrelate to random variables GMo-RTOPSIS ismore accuratelyexpressing decision-makersrsquo evaluation of alternatives andbroadens the traditional TOPSIS

The operation steps of GMo-RTOPSIS are as followsFirstly each 119863119872(119889) will provide hisher decision matrix119863119872(119889)(Y) 119889 isin 119870Secondly based on the above results the next step is

normalizing each 119863119872(119889)(Y) 119889 isin 119870 from the 119896 decision-makers Refer to (3) for normalization methods for TrFNthen 119863119872(119889)(Y)lowast 119889 isin 119870 is obtained

Thirdly calculate 119903(119889)+119895 (Y) (positive-ideal solution) and119903(119889)minus119895 (Y) (negative-ideal solution) for every119863119872(119889)(Y) 119889 isin 119870and criterion Generally there is

119903(119889)+119895 (Y) = max 119903(119889)1119895 (Y) sdot sdot sdot 119903(119889)119898119895 (Y) 119895 isin 119873 (9)

119903(119889)minus119895 (Y) = max 119903(119889)1119895 (Y) sdot sdot sdot 119903(119889)119898119895 (Y) 119895 isin 119873 (10)

Compute the separation measures for each A =(1198601 1198602 sdot sdot sdot 119860119898)119878+119894 (Y) = radic 119896sum

119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)+119895 (Y) 119903(119889)119894119895 (Y))]2119894 isin 119872

(11)


119878minus119894 (Y) = radic 119896sum119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)minus119895 (Y) 119903(119889)119894119895 (Y))]2

119894 isin 119872(12)

Among them 119908lowast119889 denotes the weight of the 119889th decision-maker based on fuzzy BWM method 119908(119889)119895 is weight of 119895thcriterion given by 119889th decision-maker in respective matrix

Fourthly we can obtain closeness coefficients for eachA = (1198601 1198602 sdot sdot sdot 119860119898) as follows

119862119862119894 = 119878minus119894 (Y)119878minus119894 (Y) + 119878+119894 (Y) (13)

Finally rank the A = (1198601 1198602 sdot sdot sdot 119860119898) using degree ofdominance 119860 119894 gt 119860119895 if 119875(119862119894(Y) gt 119862119895(Y)) gt 119875(119862119895(Y) gt119862119894(Y))54 The Main Steps of the Proposed Method The approach ofproposed method is summarized as follows

Step 1 Select the most important DM(119889119861) and least impor-tant DM(119889119882) in all decision-makers 1198891 1198892 119889119896Step 2 Compute vector of Best-to-Others AB and Others-to-Worst A119882 based on TrFN

Step 3 Calculate the optimalweight (119908lowast1 119908lowast2 sdot sdot sdot 119908lowast119896 ) of eachdecision-maker by (8)

Step 4 119896 decision-makers provide their decision matrix119863119872(119889)(Y) 119889 isin 119870 individually

Step 5 According to (3) normalize each 119863119872(119889)(Y) 119889 isin 119870from the 119896 decision-makers we get 119863119872(119889)(Y)lowast 119889 isin 119870Step 6 Calculate 119903(119889)+119895 (Y) (PIS) and 119903(119889)minus119895 (Y) (NIS) for every119863119872(119889)(Y)lowast 119889 isin 119870 and criterion by (9) and (10)

Step 7 Compute the separationmeasures 119878+119894 (Y) and 119878minus119894 (Y) foreach alternative A by (11) and (12)

Step 8 Obtain closeness coefficients 119862119862119894 for each alternativeA in (13)

Step 9 Rank the alternative A = (1198601 1198602 sdot sdot sdot 119860119898) usingdegree of dominance and select the better alternative 119860 1198946 Illustrative Examples and Discussion

61 Illustrative Example This paper takes H companyrsquos sup-plier selection in the resilient supply chain environment asan example Assuming that three decision-makers (1198891 1198892 1198893)scored four alternative suppliers (1198601 1198602 1198603 1198604) and threedecision-makers had different views on resilient supplierselection decision-maker one focused on the absorptivecapacity before the risk occurred decision-maker 2 focusedmore on how suppliers changed themselves to adapt to the

Table 2 The linguistic label for fuzzy preferences of the bestcriterion over all the criteria

Criteria 1198891 1198892 1198893Best criterion 1198891 EI VI AI

Table 3 The linguistic label for fuzzy preferences of all the criteriaover the worst criterion

Criteria Worst criterion 11988931198891 AI1198892 FI1198893 EI

environment when the disruptions occurred and decision-maker 3 considered that postdisaster reconstruction was alsothe key step to restore the normal operation of supply chainH company cannot identify the weights of the three decision-makers and M consulting company calculates the weights ofits decision-makers

There are eight criteria in total which reflect absorptivecapacity adaptive capacity and restorative capacityThe crite-ria selected by the three decision-makers can be overlappingand repetitive 1198621-surplus inventory 1198622-location separa-tion 1198623-interdependency 1198624- robustness 1198625-reliability 1198626-rerouting 1198627-reorganization and 1198628-restorationStep 1 The lsquofirst decision-makerrsquo (1198891) and lsquothird decision-makerrsquo (1198893) are respectively the best and the worst criterionbased on M companyrsquos decision

Step 2 According to the transformation rules the fuzzyreference comparisons are executed Tables 2 and 3 illustratethe fuzzy preferences of Best-to-Others and Others-to-Worstbased on Table 1 we can transfer the linguistic terms in Tables2 and 3 to membership function AB and A119882 as follows

AB = [(1 1 1) (52 3 72) (72 4 92)]A119882 = [(72 4 92) (32 2 52) (1 1 1)]

(14)

Step 3 Based on the above analysis for getting the weights ofthree decision-makers the problem can be built according to(8)

Next we bring the data from Steps 1 and 2 into theformula and get the following inequalities

min 120573lowast119904119905 100381610038161003816100381610038161003816100381610038161003816

(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)100381610038161003816100381610038161003816100381610038161003816 le (119901lowast 119901lowast 119901lowast)100381610038161003816100381610038161003816100381610038161003816


(ℎ1199081 1198961199081 1198971199081 )(ℎ1199081 1198961199081 1198971199081 ) minus (ℎ11 11989611 11989711)100381610038161003816100381610038161003816100381610038161003816 le (119901lowast 119901lowast 119901lowast)


100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)

100381610038161003816100381610038161003816100381610038161003816 le (119901lowast 119901lowast 119901lowast)100381610038161003816100381610038161003816100381610038161003816(ℎ1199082 1198961199082 1198971199082 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ23 11989623 11989723)


100381610038161003816100381610038161003816100381610038161003816 le (119901lowast 119901lowast 119901lowast)3sum119895=1

119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3

min 120573lowast119904119905 1003816100381610038161003816ℎ1 minus 35 lowast 11989731003816100381610038161003816 le 119901 lowast 119897310038161003816100381610038161198961 minus 4 lowast 11989631003816100381610038161003816 le 119901 lowast 119896310038161003816100381610038161198971 minus 45 lowast ℎ31003816100381610038161003816 le 119901 lowast ℎ31003816100381610038161003816ℎ1 minus 25 lowast 11989721003816100381610038161003816 le 119901 lowast 119897210038161003816100381610038161198961 minus 3 lowast 11989621003816100381610038161003816 le 119901 lowast 119896210038161003816100381610038161198971 minus 35 lowast ℎ21003816100381610038161003816 le 119901 lowast ℎ21003816100381610038161003816ℎ2 minus 15 lowast 11989731003816100381610038161003816 le 119901 lowast 119897310038161003816100381610038161198962 minus 2 lowast 11989631003816100381610038161003816 le 119901 lowast 119896310038161003816100381610038161198972 minus 25 lowast ℎ31003816100381610038161003816 le 119901 lowast ℎ316 lowast ℎ1 + 16 lowast 4 lowast 1198961 + 16 lowast 1198971 + 16 lowast ℎ2 + 16 lowast 4

lowast 1198962 + 16 lowast 1198972 + 16 lowast ℎ3 + 16 lowast 4 lowast 1198963 + 16 lowast 1198973= 1ℎ1 le 1198961 le 1198971

ℎ2 le 1198962 le 1198972ℎ3 le 1198963 le 1198973ℎ1 gt 0ℎ2 gt 0ℎ3 gt 0119901 ge 0(15)

Then the fuzzy weight of decision-makers is obtained bycalculating the above inequality group

119908lowast1 = (06125 06125 06458) 119908lowast2 = (02053 02315 02855)119908lowast3 = (01330 01407 01792)120573lowast = (03542 03542 03542)

(16)

Finally the crisp number of fuzzy weights is computed by(1)Therefore in the decision-making ofM company 1198891 is themost important and 1198893 is the least

119908lowast1 = 06181119908lowast2 = 02361119908lowast3 = 01458

(17)

Step 4 lsquoFirst decision-makerrsquo (1198891) selected 1198621 1198622 1198623 1198625 asthe index and lsquosecond decision-makerrsquo (1198892) thinks 1198624 1198626 1198627are the most important criteria lsquoThird decision-makerrsquo(1198893) selected indicators covering three aspects of capability1198622 1198627 1198628

And the weight vector of three decision-makers are 1199081 =(03 02 02 03) 1199082 = (02 04 04) and 1199083 = (03 04 03)The results of the three decision-makers are shown in Tables4 5 and 6

Step 5 Thenormalizedmatrix119863119872(119889)(Y)lowast 119889 isin 119870 is obtainedbased on the (3)

DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]


Table 4 Decision matrix of the first decision-maker (1198891)Alternatives 1198621 1198622 1198623 11986251198601 (0 2 3) (05 06 07) (0 01 02) (1 2 3)1198602 (4 6 7) (03 04 05) (02 03 04) (5 6 7)1198603 (2 3 4) (02 03 04) (01 02 03) (3 4 5)1198604 (7 8 9) (07 08 09) (04 05 07) (4 5 6)

Table 5 Decision matrix of the second decision-maker (1198892)Alternatives 1198624 1198626 11986271198601 (1 2 3) (03 04 05) (5 6 7)1198602 (3 4 5) (01 02 03) (4 5 6)1198603 (2 3 4) (0 01 02) (7 8 9)1198604 (6 7 8) (07 08 09) (3 4 5)

Table 6 Decision matrix of the third decision-maker (1198893)Alternatives 1198622 1198627 11986281198601 (01 02 03) (4 5 6) (0 1 2)1198602 (03 04 05) (3 4 5) (4 5 6)1198603 (02 03 04) (4 5 6) (4 5 6)1198604 (05 06 07) (2 3 4) (3 4 5)

DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)

Step 6 According to the above 119863119872(119889)(Y)lowast 119889 isin 119870 we select119903(119889)+119895 (Y) and 119903(119889)minus119895 (Y) by (9) and (10)

119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)


Table 7 Simulated separation measures and closeness coefficients

1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065

Step 7 Based on the data obtained from the above steps wecalculate the value of 119878+119894 (Y) 119878minus119894 (Y) and 119862119862119894 in Table 7

Step 8 If there are underlying factors in the decision matrixthe method using random variable will lead to differentchoices of final alternative When there is random variablein the decision matrix rank the alternatives using degree ofdominance If not the larger the 119862119894 the better the alternativeA = (1198601 1198602 sdot sdot sdot 119860119898)

According to Table 7 the rank order of the alternatives is1198604 gt 1198602 gt 1198603 gt 119860162 Discussion In this section we discuss the advantages ofthe proposed method compared with the existing supplierselection methods The specific advantages are embodied inthe following three ways(1) The evaluation results are more objective GMo-RTOPSIS method makes up for many shortcomings oftraditional TOPSIS GMo-RTOPSIS can process independentdecision-making information of multiple decision-makersat the same time so that the decision-making results arecloser to the thought of decision-makers Moreover the deci-sion matrix contains different types of information Whendescribing criteria the language of decision-makers can bemore clearly expressed(2) The weight calculation method has been improvedBWM and AHP are similar weight calculation methods butBWM greatly simplifies the process of comparisons andthe results are more convenient for consistency checkingTraditional BWMhas limitations in dealing with informationtypes Fuzzy BWM can solve the problem of weights inuncertain environments and the final weights are morerealistic(3)The fuzzy BWM in the above cases can also be used todetermine attribute weights for decision-makers

7 Conclusion

Under the environment of globalization choosing theright resilient supplier is an important part of supplychain management This paper presents a supplier selec-tion model based on the combination of fuzzy BWM andGMo-RTOPSIS Firstly the weights of decision-makers areobtained based on fuzzy BWM Secondly GMo-RTOPSISmodel is used to process the independent decision matrixprovided by decision-makers and alternatives are ranked toselect the optimal scheme

This paper contributes to the existing research fromback-ground and method (1) In the research background of otherresearchmore attention has been paid to supplier selection in

static environment or to increasing resilience by improvingsupply chain This paper focuses on supplier selection inresilient supply chain under global environment becauseglobalization makes supply chain in dynamic environmentand requires the ability to deal with disruptions immediatelyThen according to the relevant research [1 76] a compre-hensive index of resilient supplier selection under dynamicenvironment is proposed (2) In terms of research methods ahybrid multiattribute group decision-making method is pro-posed by combining fuzzy BWM and GMo-RTOPSIS Thismethod can effectively reduce the fuzziness uncertainty andsubjectivity in the decision-making process and restore thedecision-makerrsquos thought as much as possibleThemethod ofdetermining weights is improved Fuzzy BWM can get moreaccurate weights by fewer comparisons Finally the combina-tion of triangular fuzzy numbers andGMo-RTOPSIS candealwith the evaluation information of independent decision-making of multiple decision-makers in dynamic environ-ment In the process of weight determination and alternativesevaluation the data are closer to the decision-makerrsquos ideaand the decision-making process is more scientific

In addition this paper expands the research methodsof multiattribute group decision-making from two aspects(1) It makes full use of the professional knowledge ofdecision-makers and expresses their ideas more accuratelyIn the process of determining the weights of decision-makers triangular fuzzy numbers are introduced to obtainmore objective decision-maker weights (2) Hybrid researchmethods are universal This research method is suitable forsupplier selection and other multiattribute group decision-making problems such as supplier segmentation perfor-mance evaluation and risk assessment

Although with the valid study result there is workremaining to be done in the future First this work onlyfocuses on the acquisition of the weights of decision-makersand future work should focus more on the determination ofattributes weights Second future work should use empiricaldata to further testify the reasonability and scientificity of theproposed method Finally future work should be developedto support other language sets as rough sets vague sets andso on

Data Availability

The data used to support the findings of this study areavailable within the paper

Conflicts of Interest

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


Acknowledgments

This research was supported by the National Natural ScienceFoundation Council of China under Projects nos 7166305571862035 and 71502159 the Foundation of Philosophy andSocial Sciences of Yunnan Project no YB2017015 andthe Applied Basic Research Science Foundation of YunnanProvincial Department of Science and Technology underProject no 2015FD028

References

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[2] A Chavooshi A A Bahmani A Darijani A Mootab SaeiE Mehrabi and M Gholipour ldquoThe role of wood and paperindustries management of Iran in sustainable developmentrdquoJournal of Conservation andUtilization ofNatural Resources vol1 pp 79ndash95 2012

[3] F Sabouhi M S Pishvaee and M S Jabalameli ldquoResilientsupply chain design under operational and disruption risksconsidering quantity discount A case study of pharmaceuticalsupply chainrdquo Computers amp Industrial Engineering vol 126 pp657ndash672 2018

[4] R Rajesh and V Ravi ldquoSupplier selection in resilient supplychains a grey relational analysis approachrdquo Journal of CleanerProduction vol 86 no 15 pp 343ndash359 2015

[5] S Valipour Parkouhi and A Safaei Ghadikolaei ldquoA resilienceapproach for supplier selection using fuzzy analytic networkprocess and grey VIKOR techniquesrdquo Journal of Cleaner Pro-duction vol 161 pp 431ndash451 2017

[6] C S Holling ldquoResilience and stability of ecological systemsrdquoAnnual Review of Ecology Evolution and Systematics vol 4 no1 pp 1ndash23 1973

[7] Y Yang and X Xu ldquoPost-disaster grain supply chain resiliencewith government aidrdquo Transportation Research Part E Logisticsand Transportation Review vol 76 pp 139ndash159 2015

[8] S A Torabi M Baghersad and S A Mansouri ldquoResilientsupplier selection and order allocation under operational anddisruption risksrdquo Transportation Research Part E Logistics andTransportation Review vol 79 pp 22ndash48 2015

[9] S Y Ponomarov and M C Holcomb ldquoUnderstanding theconcept of supply chain resiliencerdquoThe International Journal ofLogistics Management vol 20 no 1 pp 124ndash143 2009

[10] U Juttner and S Maklan ldquoSupply chain resilience in the globalfinancial crisis An empirical studyrdquo Supply Chain ManagementReview vol 16 no 4 pp 246ndash259 2011

[11] T Papadopoulos A Gunasekaran R Dubey N Altay S JChilde and S Fosso-Wamba ldquoThe role of BigData in explainingdisaster resilience in supply chains for sustainabilityrdquo Journal ofCleaner Production vol 142 pp 1108ndash1118 2017

[12] R Rajesh ldquoTechnological capabilities and supply chainresilience of firms a relational analysis using total interpretivestructural modeling (TISM)rdquo Technological Forecasting ampSocial Change vol 118 pp 161ndash169 2017

[13] A Haldar A Ray D Banerjee and S Ghosh ldquoResilient supplierselection under a fuzzy environmentrdquo International Journal ofManagement Science and Engineering Management vol 9 no2 pp 147ndash156 2014

[14] D Pramanik A Haldar S C Mondal S K Naskar and A RayldquoResilient supplier selection using AHP-TOPSIS-QFD undera fuzzy environmentrdquo International Journal of ManagementScience and Engineering Management vol 12 no 1 pp 45ndash542016

[15] I I Mitroff and M C Alpaslan ldquoPreparing for evilrdquo HarvardBusiness Review vol 81 no 4 pp 105ndash119 2003

[16] H Peck and M Christopher ldquoBuilding the resilient supplychainrdquo The International Journal of Logistics Management vol15 no 2 pp 1ndash14 2004

[17] B Allenby and J Fink ldquoSocial and ecological resilience Towardinherently secure and resilient societiesrdquo Science vol 24 pp347ndash364 2000

[18] A L Pregenzer ldquoSystems resilience a new analytical frameworkfor nuclear nonproliferationrdquo Office of Scientific amp TechnicalInformation 2011

[19] Y Y Haimes ldquoOn the definition of resilience in systemsrdquo RiskAnalysis vol 29 no 4 pp 498ndash501 2009

[20] M Christopher and H Peck ldquoBuilding the resilient supplychainrdquo The International Journal of Logistics Management vol15 no 2 pp 1ndash14 2004

[21] P Mensah and Y Merkuryev ldquoDeveloping a resilient supplychainrdquo Procedia - Social and Behavioral Sciences vol 110 pp309ndash319 2014

[22] M C Holcomb and S Y Ponomarov ldquoUnderstanding theconcept of supply chain resiliencerdquoThe International Journal ofLogistics Management vol 20 pp 124ndash143 2009

[23] S Maklan and U Juttner ldquoSupply chain resilience in the globalfinancial crisis An empirical studyrdquo Supply Chain ManagementReview vol 16 no 4 pp 246ndash259 2011

[24] S Hosseini K Barker and J E Ramirez-Marquez ldquoA reviewof definitions and measures of system resiliencerdquo ReliabilityEngineering amp System Safety vol 145 pp 47ndash61 2016

[25] R Kumar S S Padhi and A Sarkar ldquoSupplier selectionof an Indian heavy locomotive manufacturer an integratedapproach using taguchi loss function TOPSIS and AHPrdquo IIMBManagement Review 2018

[26] G Buyukozkan and S Guleryuz ldquoA new integrated intuition-istic fuzzy group decision making approach for product devel-opment partner selectionrdquoComputers amp Industrial Engineeringvol 102 pp 383ndash395 2016

[27] J S Baek A Meroni and E Manzini ldquoA socio-technicalapproach to design for community resilience A framework foranalysis and design goal formingrdquo Design Studies vol 40 pp60ndash84 2015

[28] P Tamvakis and Y Xenidis ldquoResilience in transportationsystemsrdquo Procedia - Social and Behavioral Sciences vol 48 pp3441ndash3450 2012

[29] E D Vugrin D E Warren and M A Ehlen ldquoA resilienceassessment framework for infrastructure and economic sys-tems Quantitative and qualitative resilience analysis of petro-chemical supply chains to a hurricanerdquo Process Safety Progressvol 30 no 3 pp 280ndash290 2011

[30] S Hosseini A Al Khaled and M D Sarder ldquoA generalframework for assessing system resilience using Bayesian net-works A case study of sulfuric acid manufacturerrdquo Journal ofManufacturing Systems vol 41 pp 211ndash227 2016

[31] S Hosseini and K Barker ldquoA Bayesian network model forresilience-based supplier selectionrdquo International Journal ofProduction Economics vol 180 pp 68ndash87 2016


[32] S Hosseini and K Barker ldquoModeling infrastructure resilienceusing Bayesian networks A case study of inland waterwayportsrdquoComputersamp Industrial Engineering vol 93 pp 252ndash2662016

[33] B M Dos Santos L P Godoy and L M S Campos ldquoPerfor-mance evaluation of green suppliers using entropy-TOPSIS-FrdquoJournal of Cleaner Production vol 207 pp 498ndash509 2019

[34] A Memari A Dargi M R Akbari Jokar R Ahmad and A RAbdul Rahim ldquoSustainable supplier selection A multi-criteriaintuitionistic fuzzy TOPSIS methodrdquo Journal of ManufacturingSystems vol 50 p 24 2019

[35] C Yu Y Shao K Wang and L Zhang ldquoA group decisionmaking sustainable supplier selection approach using extendedTOPSIS under interval-valued Pythagorean fuzzy environ-mentrdquo Expert Systems with Applications vol 121 pp 1ndash17 2019

[36] Z Chen and W Yang ldquoAn MAGDM based on constrainedFAHP and FTOPSIS and its application to supplier selectionrdquoMathematical and Computer Modelling vol 54 no 11-12 pp2802ndash2815 2011

[37] A Dargi A Anjomshoae M R Galankashi A Memari andM B M Tap ldquoSupplier selection A fuzzy-ANP approachrdquo inProceedings of the 2nd International Conference on InformationTechnology and Quanttative Management (ITQM rsquo14) vol 31pp 691ndash700 Russia June 2014

[38] S K Jauhar andM Pant ldquoIntegratingDEAwithDE andMODEfor sustainable supplier selectionrdquo Journal of ComputationalScience vol 21 pp 299ndash306 2017

[39] I Dobos and G Vorosmarty ldquoInventory-related costs in greensupplier selection problems with data envelopment analysis(DEA)rdquo International Journal of Production Economics 2018

[40] K Rashidi and K Cullinane ldquoA comparison of fuzzy DEA andfuzzy TOPSIS in sustainable supplier selection Implications forsourcing strategyrdquoExpert Systems with Applications vol 121 pp266ndash281 2019

[41] YWu K Chen B Zeng H Xu and Y Yang ldquoSupplier selectionin nuclearpower industrywith extendedVIKORmethodunderlinguistic informationrdquo Applied Soft Computing vol 48 pp444ndash457 2016

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

[43] J Rezaei J Wang and L Tavasszy ldquoLinking supplier devel-opment to supplier segmentation using Best Worst MethodrdquoExpert Systems with Applications vol 42 no 23 pp 9152ndash91642015

[44] H Gupta andM K Barua ldquoSupplier selection among SMEs onthe basis of their green innovation ability using BWMand fuzzyTOPSISrdquo Journal of Cleaner Production vol 152 pp 242ndash2582017

[45] J Rezaei ldquoBest-worst multi-criteria decision-making methodrdquoOmega vol 53 pp 49ndash57 2015

[46] J Rezaei ldquoBest-worst multi-criteria decision-making methodsome properties and a linear modelrdquo Omega vol 64 pp 126ndash130 2016

[47] Z-P Tian J-Q Wang and H-Y Zhang ldquoAn integratedapproach for failure mode and effects analysis based on fuzzybest-worst relative entropy and VIKORmethodsrdquo Applied SoftComputing vol 72 pp 636ndash646 2018

[48] S Guo and H Zhao ldquoFuzzy best-worst multi-criteria decision-makingmethod and its applicationsrdquoKnowledge-Based Systemsvol 121 pp 23ndash31 2017

[49] A Hafezalkotob and A Hafezalkotob ldquoA novel approach forcombination of individual and group decisions based on fuzzybest-worst methodrdquo Applied Soft Computing vol 59 pp 316ndash325 2017

[50] Z-P Tian J-Q Wang J Wang and H-Y Zhang ldquoA multi-phase QFD-based hybrid fuzzy MCDM approach for perfor-mance evaluation A case of smart bike-sharing programs inChangshardquo Journal of Cleaner Production vol 171 pp 1068ndash1083 2018

[51] J Rezaei O Kothadiya L Tavasszy and M Kroesen ldquoQual-ity assessment of airline baggage handling systems usingSERVQUAL and BWMrdquo Tourism Management vol 66 pp 85ndash93 2018

[52] F Nawaz M R Asadabadi N K Janjua O K Hussain EChang and M Saberi ldquoAn MCDM method for cloud serviceselection using a Markov chain and the best-worst methodrdquoKnowledge-Based Systems vol 159 pp 120ndash131 2018

[53] G Van de Kaa M Janssen and J Rezaei ldquoStandards battlesfor business-to-government data exchange Identifying successfactors for standard dominance using the best worst methodrdquoTechnological Forecasting amp Social Change vol 137 pp 182ndash1892018

[54] P Shojaei S A Seyed Haeri and S Mohammadi ldquoAirportsevaluation and rankingmodel usingTaguchi loss function best-worst method and VIKOR techniquerdquo Journal of Air TransportManagement vol 68 pp 4ndash13 2018

[55] N Salimi and J Rezaei ldquoEvaluating firmsrsquo RampD performanceusing best worst methodrdquo Evaluation and Program Planningvol 66 pp 147ndash155 2018

[56] J Ren H Liang and F T S Chan ldquoUrban sewage sludgesustainability and transition for Eco-City Multi-criteria sus-tainability assessment of technologies based on best-worstmethodrdquoTechnological Forecasting amp Social Change vol 116 pp29ndash39 2017

[57] C-L Hwang and K YoonMultiple Attributes Decision MakingMethods and Applications New York NY USA 1981

[58] G R Jahanshahloo F Hosseinzadeh Lotfi and A R DavoodildquoExtension of TOPSIS for decision-making problems withinterval data interval efficiencyrdquo Mathematical and ComputerModelling vol 49 no 5-6 pp 1137ndash1142 2009

[59] Z Yue ldquoAn extended TOPSIS for determining weights of deci-sion makers with interval numbersrdquo Knowledge-Based Systemsvol 24 no 1 pp 146ndash153 2011

[60] L Dymova P Sevastjanov and A Tikhonenko ldquoA directinterval extension of TOPSIS methodrdquo Expert Systems withApplications vol 40 no 12 pp 4841ndash4847 2013

[61] C Chen ldquoExtensions of the TOPSIS for group decision-makingunder fuzzy environmentrdquo Fuzzy Sets and Systems vol 114 no1 pp 1ndash9 2000

[62] R A Krohling andVC Campanharo ldquoFuzzyTOPSIS for groupdecision making a case study for accidents with oil spill in theseardquo Expert Systems with Applications vol 38 no 4 pp 4190ndash4197 2011

[63] G Lee K S Jun and E-S Chung ldquoRobust spatial floodvulnerability assessment forHanRiver using fuzzyTOPSISwith120572-cut level setrdquo Expert Systems with Applications vol 41 no 2pp 644ndash654 2014

[64] F E Boran S Genc M Kurt and D Akay ldquoA multi-criteriaintuitionistic fuzzy group decisionmaking for supplier selectionwith TOPSISmethodrdquoExpert Systems with Applications vol 36no 8 pp 11363ndash11368 2009


[65] H Shih H Shyur and E S Lee ldquoAn extension of TOPSISfor group decision makingrdquoMathematical and Computer Mod-elling vol 45 no 7-8 pp 801ndash813 2007

[66] D-F Li Z-G Huang and G-H Chen ldquoA systematic approachto heterogeneous multiattribute group decision makingrdquo Com-puters amp Industrial Engineering vol 59 pp 561ndash572 2010

[67] B Vahdani S M Mousavi and R Tavakkoli-MoghaddamldquoGroup decisionmaking based on novel fuzzymodifiedTOPSISmethodrdquo Applied Mathematical Modelling vol 35 no 9 pp4257ndash4269 2011

[68] R Lourenzutti and R A Krohling ldquoA generalized TOPSISmethod for group decision making with heterogeneous infor-mation in a dynamic environmentrdquo Information Sciences vol330 pp 1ndash18 2016

[69] S H Zanakis A Solomon N Wishart and S Dublish ldquoMulti-attribute decision making a simulation comparison of selectmethodsrdquo European Journal of Operational Research vol 107no 3 pp 507ndash529 1998

[70] A-H Peng and X-M Xiao ldquoMaterial selection usingPROMETHEE combined with analytic network processunder hybrid environmentrdquo Materials and Corrosion vol 47pp 643ndash652 2013

[71] X Sun V Gollnick Y Li and E Stumpf ldquoIntelligent multi-criteria decision support system for systems designrdquo Journal ofAircraft vol 51 pp 216ndash225 2014

[72] S H Mousavi-Nasab and A Sotoudeh-Anvari ldquoA comprehen-siveMCDM-based approach usingTOPSIS COPRAS andDEAas an auxiliary tool for material selection problemsrdquo Materialsand Corrosion vol 121 pp 237ndash253 2017

[73] I Eusgeld W Kroger G Sansavini M Schlapfer and E ZioldquoThe role of network theory and object-oriented modelingwithin a framework for the vulnerability analysis of criticalinfrastructuresrdquoReliability Engineering amp System Safety vol 94no 5 pp 954ndash963 2009

[74] J Johansson andHHassel ldquoAn approach formodelling interde-pendent infrastructures in the context of vulnerability analysisrdquoReliability Engineering amp System Safety vol 95 no 12 pp 1335ndash1344 2010

[75] J JohanssonHHassel andE Zio ldquoReliability and vulnerabilityanalyses of critical infrastructures Comparing two approachesin the context of power systemsrdquo Reliability Engineering ampSystem Safety vol 120 pp 27ndash38 2013

[76] S Hosseini and A A Khaled ldquoA hybrid ensemble and AHPapproach for resilient supplier selectionrdquo Journal of IntelligentManufacturing pp 1ndash22 2016

[77] D D Wu Y Zhang and D L Olson ldquoFuzzy multi-objectiveprogramming for supplier selection and risk modeling apossibility approachrdquoEuropean Journal ofOperational Researchvol 200 no 3 pp 774ndash787 2010

[78] M Christopher Logistics and Supply Chain ManagementFinancial TimesPrentice Hall 2010

[79] M Mellat-Parast ldquoDeveloping a resilient supply chain throughsupplier flexibility and reliability assessmentrdquo InternationalJournal of Production Research vol 54 no 1 pp 302ndash321 2016

[80] R Reyes Levalle and S Y Nof ldquoResilience by teaming in supplynetwork formation and re-configurationrdquo International Journalof Production Economics vol 160 pp 80ndash93 2015

[81] J Toyli A Wieland and C M Wallenburg ldquoThe influence ofrelational competencies on supply chain resilience a relationalviewrdquo International Journal of Physical Distribution LogisticsManagement vol 43 pp 300ndash320 2013

[82] S K Mahapatra R Narasimhan and P Barbieri ldquoStrate-gic interdependence governance effectiveness and supplierperformance A dyadic case study investigation and theorydevelopmentrdquo Journal of Operations Management vol 28 no6 pp 537ndash552 2010

[83] L A Zadeh ldquoFuzzy setsrdquo Information and Computation vol 8pp 338ndash353 1965

[84] S H Chen and CH Hsieh ldquoRepresentation ranking distanceand similarity of L-R type fuzzy number and applicationrdquoAustralian Journal of Intelligent Processing Systems vol 6 pp217ndash229 2000

[85] H Zhao and S Guo ldquoSelecting green supplier of thermal powerequipment by using a hybridMCDMmethod for sustainabilityrdquoSustainability vol 6 no 1 pp 217ndash235 2014

[86] M Dagdeviren S Yavuz and N Kilinc ldquoWeapon selectionusing the AHP and TOPSIS methods under fuzzy environ-mentrdquoExpert Systems with Applications vol 36 no 4 pp 8143ndash8151 2009

[87] F A Lootsma ldquoSaatyrsquos priority theory and the nomination ofa senior professor in operations Researchrdquo European Journal ofOperational Research vol 4 no 6 pp 380ndash388 1980

[88] C L Hwang and K P Yoon Multiple Attributes DecisionMaking Methods and Applications 1981

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visibility as indicators and determined supplierrsquos elasticitylevel by combining fuzzy analysis network process and greyVIKOR Haldar et al [13] combined fuzzy TOPSIS and fuzzyweight method to select resilient suppliers which can reducethe vulnerability of supply chain system Pramanik et al [14]uses AHP-TOPSIS-QFD to measure supplier performance inorder to select a resilient supplier

However through literature review we find that the sup-plier selection in resilient supply chain still has limitationsFirstly few studies have been conducted on the selection ofresilient suppliers Secondly many multiattribute decision-making methods strongly restrict the freedom of decision-makers to use the type of information which greatly reducesthe personal opinions of relevant decision-makersThirdly inmost studies decision-makers have to reach an agreement oncriteria which is difficult to achieve Fourthly crisp numbercannot accurately describe the decision-makerrsquos evaluation ofalternatives Therefore in order to fill the research gap weproposed a method combining fuzzy BWM and improvedTOPSIS to determine the weight of decision-makers and rankthe alternatives for supplier selection in resilient supply chainFinally the practicability of this method is proved by theillustrative example

The structure of this paper is divided into seven partsThe second section is literature review the third sectionproposes the evaluation criteria of resilient supplier selectionunder supply chain environment Section four introducesthe preliminaries including some definitions The proposedmethod is proposed in the fifth section Section six introducesthe illustrative example Finally the conclusions are presentedin section seven

2 Literature Review

Some early researchers defined resilience as the ability of asystem to recover from disruption [15 16] In the definitionof resilience by scholars Allenby and Fink [17] and Pregenzer[18] the ability of the system to maintain function in thedisaster is emphasized Haimes [19] proposed the definitionof resilience refers to the ability of withstand the disruptionand recovery with reasonable time and costs After thatscholars state that the key to enhancing resilience is that thesupply chain process should bemanaged and put forward theprinciple of building a resilient supply chain [20 21] Hol-comb and Ponomarov [22] proposed that logistics capacity isrelated to resilience coordination and integration capabilitiescan enhance the ability to confront disruption Maklan andJuttner [23] argued that risk management and knowledgemanagement have an impact on resilience Hosseini et al[24] proposed the method of literature classification andthrough literature review studied the application domain ofresilience and identified four areas of resilient applicationorganizational domain social domain economic domainand engineering domain Papadopoulos et al [11] emphasizedthe role of swift trust public-private partnerships and qualityof information sharing in promoting supply chain resilience

Supplier selection is an important issue in the resilientsupply chain and daily operation of enterprises It is regarded

as a strategic choice of enterprises [25] and also a difficultand complex process [26] In the 1990s scholars beganto study the selection of business suppliers Subsequentlyscholars subdivided the selection of suppliers such as thechoice of sustainable suppliers and resilient suppliers andthe criteria considered in the selection process changedaccordingly However scholars have not reached a consensuson the selection criteria of resilient suppliers Christopherand Peck [20] discussed the upstream inventory and supplyconditions on impact of supply chain resilience Rajesh andRavi [4] considered that when choosing resilient suppliersthe key factors that should be considered include vul-nerability collaboration risk awareness and supply chaincontinuity management Baek et al [27] argued that thedriving factor of resilient supply chain is flexibility whileTamvakis et al [28] emphasize the role of transportationVugrin et al [29] define resilience from the perspectives ofpredisruption prevention and postdisruption recovery andconsidered that resilience includes absorptive adaptive andrestorative capacities Scholar Hosseini extends the contentof resilience subdivides the criteria of absorptive adaptiveand restorative capacities in different application domainquantifies the resilience of inland waterway ports and sulfuricacid manufacturer with Bayesian network and studies theselection of resilient suppliers [30ndash32]

Supplier selection essentially is a multiattribute decision-making problem and there are many methods to deal withsuch problems in the field of supply chain for exampleTechnique for Order Preference by Similarity to Ideal Solu-tion (TOPSIS) and improved TOPSIS [25 33ndash35] AnalyticHierarchy Process (AHP) and its extension [25 26 36] ANP[37]Data Envelopment Analysis (DEA) and its improvement[38ndash40] VIKOR [5 41 42] and best-worst multicriteriadecision-making method (BWM) [43 44] BWM has onlybeen proposed in recent years the relevant research isrelatively blank which is a direction of great research value

BWM is proposed by Rezaei [45] compared with AHPBWM needs less data for comparison and the final resultis consistent with AHP [46] BWM greatly reduces thecomplexity of calculation And throughmore consistent com-parisons the final result will be more credible However thetraditional BWM cannot determine the weight in uncertainenvironment [47] so scholars have improved BWM andfuzzy BWM has been developed [48ndash50] BWM based ontriangular fuzzy numbers is one of them BWM has beenused in many areas and has solved some practical problemssuch as evaluating the service quality of baggage handlingsystems [51] cloud service selection [52] identifying successfactors in eXtensible Business Reporting Language (XBRL)[53] performance evaluation and ranking of airports [54]identifying the research and development (RampD) of enter-prises [55] assessment of the technologies for the treatmentof urban sewage sludge [56] etc

As a common method TOPSIS is proposed by Hwangand Yoon [57] The principle of TOPSIS is to make the idealsolution as close to positive-ideal solution (PIS) as possibleand as far away fromnegative-ideal solution (NIS) as possibleHowever the traditional TOPSIS still has some limitations Itcan only deal with the information of a single decision-maker











Adaptive capacity

Surplus inventory


Absorptive capacity

Location separation

Reliability

Robustness

Interdependency

Rerouting

Reorganization

Restoration

Crite

ria o

f Res

ilien

t Sup

plie

r Sel

ectio

n



















4 Preliminaries





119877 (119886) = 1198861 + 41198862 + 11988636 (1)


119889 (119886 ) = radic 133sum119894=1

(119886119894 minus 119887119894)2 (2)


119903119894119895 = ( 1198861119894119895max119894 1198863119894119895

1198862119894119895max119894 1198863119894119895





Improvement of BWM


Aggregation stage



Selection stage



Preparation stage

Fuzzy BWM


GMo-RTOPSIS





=11986011198602119860119898

1198621 1198622 sdot sdot sdot 119862119899[[[[[[[[

119904(119889)11 (Y(119889))119904(119889)21 (Y(119889))119904(119889)1198981 (Y(119889))

119904(119889)12 (Y(119889))119904(119889)22 (Y(119889))119904(119889)1198982 (Y(119889))


119904(119889)1119899 (Y(119889))119904(119889)2119899 (Y(119889))119904(119889)119898119899 (Y(119889))

]]]]]]]]

119889 = 1 sdot sdot sdot 119896

(4)






AB = (1198861198611 1198861198612 sdot sdot sdot 119886119861119896) (5)

A119882 = (1198861119882 1198862119882 sdot sdot sdot 119886119896119882) (6)









min 120573119904119905 1003816100381610038161003816100381610038161003816100381610038161003816

119908119861119908119895 minus 1198861198611198951003816100381610038161003816100381610038161003816100381610038161003816 le 120573100381610038161003816100381610038161003816100381610038161003816

119908119895119908119882 minus 119886119895119882100381610038161003816100381610038161003816100381610038161003816 le 120573

119899sum119895=1


(7)



min 120573lowast119904119905 10038161003816100381610038161003816100381610038161003816100381610038161003816

(ℎ119908119861 119896119908119861 119897119908119861 )(ℎ119908119895 119896119908119895 119897119908119895 ) minus (ℎ119861119895 119896119861119895 119897119861119895)10038161003816100381610038161003816100381610038161003816100381610038161003816 le (119901



119899sum119895=1

119877 (119908119895) = 1


(8)









119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)+119895 (Y) 119903(119889)119894119895 (Y))]2119894 isin 119872

(11)


119878minus119894 (Y) = radic 119896sum119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)minus119895 (Y) 119903(119889)119894119895 (Y))]2

119894 isin 119872(12)



119862119862119894 = 119878minus119894 (Y)119878minus119894 (Y) + 119878+119894 (Y) (13)

















AB = [(1 1 1) (52 3 72) (72 4 92)]A119882 = [(72 4 92) (32 2 52) (1 1 1)]

(14)



min 120573lowast119904119905 100381610038161003816100381610038161003816100381610038161003816





100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)




119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3






(16)



(17)




DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]





DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018


















Adaptive capacity

Surplus inventory


Absorptive capacity

Location separation

Reliability

Robustness

Interdependency

Rerouting

Reorganization

Restoration

Crite

ria o

f Res

ilien

t Sup

plie

r Sel

ectio

n



















4 Preliminaries





119877 (119886) = 1198861 + 41198862 + 11988636 (1)


119889 (119886 ) = radic 133sum119894=1

(119886119894 minus 119887119894)2 (2)


119903119894119895 = ( 1198861119894119895max119894 1198863119894119895

1198862119894119895max119894 1198863119894119895





Improvement of BWM


Aggregation stage



Selection stage



Preparation stage

Fuzzy BWM


GMo-RTOPSIS





=11986011198602119860119898

1198621 1198622 sdot sdot sdot 119862119899[[[[[[[[

119904(119889)11 (Y(119889))119904(119889)21 (Y(119889))119904(119889)1198981 (Y(119889))

119904(119889)12 (Y(119889))119904(119889)22 (Y(119889))119904(119889)1198982 (Y(119889))


119904(119889)1119899 (Y(119889))119904(119889)2119899 (Y(119889))119904(119889)119898119899 (Y(119889))

]]]]]]]]

119889 = 1 sdot sdot sdot 119896

(4)






AB = (1198861198611 1198861198612 sdot sdot sdot 119886119861119896) (5)

A119882 = (1198861119882 1198862119882 sdot sdot sdot 119886119896119882) (6)









min 120573119904119905 1003816100381610038161003816100381610038161003816100381610038161003816

119908119861119908119895 minus 1198861198611198951003816100381610038161003816100381610038161003816100381610038161003816 le 120573100381610038161003816100381610038161003816100381610038161003816

119908119895119908119882 minus 119886119895119882100381610038161003816100381610038161003816100381610038161003816 le 120573

119899sum119895=1


(7)



min 120573lowast119904119905 10038161003816100381610038161003816100381610038161003816100381610038161003816

(ℎ119908119861 119896119908119861 119897119908119861 )(ℎ119908119895 119896119908119895 119897119908119895 ) minus (ℎ119861119895 119896119861119895 119897119861119895)10038161003816100381610038161003816100381610038161003816100381610038161003816 le (119901



119899sum119895=1

119877 (119908119895) = 1


(8)









119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)+119895 (Y) 119903(119889)119894119895 (Y))]2119894 isin 119872

(11)


119878minus119894 (Y) = radic 119896sum119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)minus119895 (Y) 119903(119889)119894119895 (Y))]2

119894 isin 119872(12)



119862119862119894 = 119878minus119894 (Y)119878minus119894 (Y) + 119878+119894 (Y) (13)

















AB = [(1 1 1) (52 3 72) (72 4 92)]A119882 = [(72 4 92) (32 2 52) (1 1 1)]

(14)



min 120573lowast119904119905 100381610038161003816100381610038161003816100381610038161003816





100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)




119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3






(16)



(17)




DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]





DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018
















4 Preliminaries





119877 (119886) = 1198861 + 41198862 + 11988636 (1)


119889 (119886 ) = radic 133sum119894=1

(119886119894 minus 119887119894)2 (2)


119903119894119895 = ( 1198861119894119895max119894 1198863119894119895

1198862119894119895max119894 1198863119894119895





Improvement of BWM


Aggregation stage



Selection stage



Preparation stage

Fuzzy BWM


GMo-RTOPSIS





=11986011198602119860119898

1198621 1198622 sdot sdot sdot 119862119899[[[[[[[[

119904(119889)11 (Y(119889))119904(119889)21 (Y(119889))119904(119889)1198981 (Y(119889))

119904(119889)12 (Y(119889))119904(119889)22 (Y(119889))119904(119889)1198982 (Y(119889))


119904(119889)1119899 (Y(119889))119904(119889)2119899 (Y(119889))119904(119889)119898119899 (Y(119889))

]]]]]]]]

119889 = 1 sdot sdot sdot 119896

(4)






AB = (1198861198611 1198861198612 sdot sdot sdot 119886119861119896) (5)

A119882 = (1198861119882 1198862119882 sdot sdot sdot 119886119896119882) (6)









min 120573119904119905 1003816100381610038161003816100381610038161003816100381610038161003816

119908119861119908119895 minus 1198861198611198951003816100381610038161003816100381610038161003816100381610038161003816 le 120573100381610038161003816100381610038161003816100381610038161003816

119908119895119908119882 minus 119886119895119882100381610038161003816100381610038161003816100381610038161003816 le 120573

119899sum119895=1


(7)



min 120573lowast119904119905 10038161003816100381610038161003816100381610038161003816100381610038161003816

(ℎ119908119861 119896119908119861 119897119908119861 )(ℎ119908119895 119896119908119895 119897119908119895 ) minus (ℎ119861119895 119896119861119895 119897119861119895)10038161003816100381610038161003816100381610038161003816100381610038161003816 le (119901



119899sum119895=1

119877 (119908119895) = 1


(8)









119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)+119895 (Y) 119903(119889)119894119895 (Y))]2119894 isin 119872

(11)


119878minus119894 (Y) = radic 119896sum119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)minus119895 (Y) 119903(119889)119894119895 (Y))]2

119894 isin 119872(12)



119862119862119894 = 119878minus119894 (Y)119878minus119894 (Y) + 119878+119894 (Y) (13)

















AB = [(1 1 1) (52 3 72) (72 4 92)]A119882 = [(72 4 92) (32 2 52) (1 1 1)]

(14)



min 120573lowast119904119905 100381610038161003816100381610038161003816100381610038161003816





100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)




119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3






(16)



(17)




DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]





DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018









Improvement of BWM


Aggregation stage



Selection stage



Preparation stage

Fuzzy BWM


GMo-RTOPSIS





=11986011198602119860119898

1198621 1198622 sdot sdot sdot 119862119899[[[[[[[[

119904(119889)11 (Y(119889))119904(119889)21 (Y(119889))119904(119889)1198981 (Y(119889))

119904(119889)12 (Y(119889))119904(119889)22 (Y(119889))119904(119889)1198982 (Y(119889))


119904(119889)1119899 (Y(119889))119904(119889)2119899 (Y(119889))119904(119889)119898119899 (Y(119889))

]]]]]]]]

119889 = 1 sdot sdot sdot 119896

(4)






AB = (1198861198611 1198861198612 sdot sdot sdot 119886119861119896) (5)

A119882 = (1198861119882 1198862119882 sdot sdot sdot 119886119896119882) (6)









min 120573119904119905 1003816100381610038161003816100381610038161003816100381610038161003816

119908119861119908119895 minus 1198861198611198951003816100381610038161003816100381610038161003816100381610038161003816 le 120573100381610038161003816100381610038161003816100381610038161003816

119908119895119908119882 minus 119886119895119882100381610038161003816100381610038161003816100381610038161003816 le 120573

119899sum119895=1


(7)



min 120573lowast119904119905 10038161003816100381610038161003816100381610038161003816100381610038161003816

(ℎ119908119861 119896119908119861 119897119908119861 )(ℎ119908119895 119896119908119895 119897119908119895 ) minus (ℎ119861119895 119896119861119895 119897119861119895)10038161003816100381610038161003816100381610038161003816100381610038161003816 le (119901



119899sum119895=1

119877 (119908119895) = 1


(8)









119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)+119895 (Y) 119903(119889)119894119895 (Y))]2119894 isin 119872

(11)


119878minus119894 (Y) = radic 119896sum119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)minus119895 (Y) 119903(119889)119894119895 (Y))]2

119894 isin 119872(12)



119862119862119894 = 119878minus119894 (Y)119878minus119894 (Y) + 119878+119894 (Y) (13)

















AB = [(1 1 1) (52 3 72) (72 4 92)]A119882 = [(72 4 92) (32 2 52) (1 1 1)]

(14)



min 120573lowast119904119905 100381610038161003816100381610038161003816100381610038161003816





100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)




119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3






(16)



(17)




DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]





DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018















min 120573119904119905 1003816100381610038161003816100381610038161003816100381610038161003816

119908119861119908119895 minus 1198861198611198951003816100381610038161003816100381610038161003816100381610038161003816 le 120573100381610038161003816100381610038161003816100381610038161003816

119908119895119908119882 minus 119886119895119882100381610038161003816100381610038161003816100381610038161003816 le 120573

119899sum119895=1


(7)



min 120573lowast119904119905 10038161003816100381610038161003816100381610038161003816100381610038161003816

(ℎ119908119861 119896119908119861 119897119908119861 )(ℎ119908119895 119896119908119895 119897119908119895 ) minus (ℎ119861119895 119896119861119895 119897119861119895)10038161003816100381610038161003816100381610038161003816100381610038161003816 le (119901



119899sum119895=1

119877 (119908119895) = 1


(8)









119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)+119895 (Y) 119903(119889)119894119895 (Y))]2119894 isin 119872

(11)


119878minus119894 (Y) = radic 119896sum119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)minus119895 (Y) 119903(119889)119894119895 (Y))]2

119894 isin 119872(12)



119862119862119894 = 119878minus119894 (Y)119878minus119894 (Y) + 119878+119894 (Y) (13)

















AB = [(1 1 1) (52 3 72) (72 4 92)]A119882 = [(72 4 92) (32 2 52) (1 1 1)]

(14)



min 120573lowast119904119905 100381610038161003816100381610038161003816100381610038161003816





100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)




119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3






(16)



(17)




DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]





DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018









119878minus119894 (Y) = radic 119896sum119889=1

119899119889sum119895=1

[119908lowast119889119908(119889)119895 119889 (119903(119889)minus119895 (Y) 119903(119889)119894119895 (Y))]2

119894 isin 119872(12)



119862119862119894 = 119878minus119894 (Y)119878minus119894 (Y) + 119878+119894 (Y) (13)

















AB = [(1 1 1) (52 3 72) (72 4 92)]A119882 = [(72 4 92) (32 2 52) (1 1 1)]

(14)



min 120573lowast119904119905 100381610038161003816100381610038161003816100381610038161003816





100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)




119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3






(16)



(17)




DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]





DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018









100381610038161003816100381610038161003816100381610038161003816(ℎ1199081 1198961199081 1198971199081 )(ℎ1199083 1198961199083 1198971199083 ) minus (ℎ13 11989613 11989713)




119877 (119908119895) = 1ℎ119908119895 le 119896119908119895 le 119897119908119895ℎ119908119895 ge 0119895 = 1 2 3






(16)



(17)




DM(1) (Y(1))lowast =1198601119860211986031198604

1198621 1198622 1198623 1198625[[[[[[[[[[[[

(0 29 39)(49 69 79)(29 39 49)(79 89 1)

(0509 0609 0709)(0309 0409 0509)(0209 0309 0409)(0709 0809 0909)

(0 0107 0207)(0207 0307 0407)(0107 0207 0307)(0407 0507 0707)

(17 27 37)(57 67 1)(37 47 57)(47 57 67)

]]]]]]]]]]]]





DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018












DM(2) (Y(2))lowast =1198601119860211986031198604

1198624 1198626 1198627[[[[[[[[[[

(18 28 38)(38 48 58)(28 38 48)(68 78 88)

(0309 0409 0509)(0109 0209 0309)(0 0109 0209)(0709 0809 0909)

(59 69 79)(49 59 69)(79 89 1)(39 49 59)

]]]]]]]]]]

DM(3) (Y(3))lowast =1198601119860211986031198604

1198622 1198627 1198628[[[[[[[[[[

(0107 0207 0307)(0307 0407 0507)(0207 0307 0407)(0507 0607 1)

(46 56 1)(36 46 56)(46 56 1)(26 36 46)

(0 16 26)(46 56 1)(46 56 1)(36 46 56)

]]]]]]]]]](18)


119903(1)+119895 (Y)= [(79 89 1) (0709 0809 0909) (0407 0507 0707) (57 67 1)]119903(1)minus119895 (Y)= [(0 29 39) (0209 0309 0409) (0 0107 0207) (17 27 37)]

119903(2)+119895 (Y) = [(68 78 88) (0709 0809 0909) (79 89 1)]119903(2)minus119895 (Y) = [(18 28 38) (0 0109 0209) (39 49 59)]119903(3)+119895 (Y) = [(0507 0607 1) (46 56 1) (46 56 1)]119903(3)minus119895 (Y) = [(0107 0207 0307) (26 36 46) (0 16 26)]

(19)



1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018










1198601 1198602 1198603 1198604119878+ (y) 0279 0171 0244 009119878minus (y) 0098 0192 0183 0168119862119862 (y) 026 053 043 065




7 Conclusion






Data Availability





Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018









Acknowledgments


References


































































































Journal of












Journal of







Volume 2018






Volume 2018










































































Journal of












Journal of







Volume 2018






Volume 2018








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