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(cid:2) AHandbookonMulti-AttributeDecision-MakingMethods (cid:2) (cid:2) (cid:2) (cid:2) Wiley Series in Operations Research and Management Science OperationsResearchandManagementScience(ORMS)isabroad, interdisciplinarybranchofappliedmathematicsconcernedwithimproving thequalityofdecisionsandprocessesandisamajorcomponentoftheglobal modernmovementtowardtheuseofadvancedanalyticsinindustryand scientificresearch.TheWileySeriesinOperationsResearchandManagement Sciencefeaturesabroadcollectionofbooksthatmeetthevariedneedsof researchers,practitioners,policymakers,andstudentswhouseorneedto improvetheiruseofanalytics.Reflectingthewiderangeofcurrentresearch withintheORMScommunity,theSeriesencompassesapplication, methodology,andtheoryandprovidescoverageofbothclassicalandcutting edgeORMSconceptsanddevelopments.Writtenbyrecognizedinternational expertsinthefield,thiscollectionisappropriateforstudentsaswellas professionalsfromprivateandpublicsectorsincludingindustry, government,andnonprofitorganizationwhoareinterestedinORMSata technicallevel.TheSeriesiscomprisedoffoursections:Analytics;Decision andRiskAnalysis;OptimizationModels;andStochasticModels. AdvisoryEditors•DecisionandRiskAnalysis (cid:2) (cid:2) GilbertoMontibeller,LondonSchoolofEconomics GregoryS.Parnell,UnitedStatesMilitaryAcademyatWestPoint FoundingSeriesEditor JamesJ.Cochran,UniversityofAlabama Analytics YangandLee•HealthcareAnalytics:FromDatatoKnowledgetoHealthcare Improvement ForthcomingTitles Attoh-Okine•BigDataandDifferentialPrivacy:AnalysisStrategiesfor RailwayTrackEngineering KongandZhang•DecisionAnalyticsandOptimizationinDiseasePrevention andTreatment DecisionandRiskAnalysis Barron•GameTheory:AnIntroduction,SecondEdition Bozorg-Haddad,Zolghadr-Asli,andLoáiciga•AHandbookon Multi-AttributeDecision-MakingMethods (cid:2) (cid:2) Brailsford,Churilov,andDangerfield•Discrete-EventSimulationandSystem DynamicsforManagementDecisionMaking Johnson,Keisler,Solak,Turcotte,Bayram,andDrew•DecisionSciencefor HousingandCommunityDevelopment:LocalizedandEvidence-Based ResponsestoDistressedHousingandBlightedCommunities MislickandNussbaum•CostEstimation:MethodsandTools ForthcomingTitles AlemanandCarter•HealthcareEngineering OptimizationModels Ghiani,Laporte,andMusmanno•IntroductiontoLogisticsSystems Management,SecondEdition ForthcomingTitles Smith•LearningOperationsResearchThroughPuzzlesandGames Tone•AdvancesinDEATheoryandApplications:WithExamplesin ForecastingModels StochasticModels (cid:2) (cid:2) Ibe•RandomWalkandDiffusionProcesses ForthcomingTitles Donohue,Katok,andLeider•TheHandbookofBehavioralOperations Matis•AppliedMarkovBasedModellingofRandomProcesses (cid:2) (cid:2) A Handbook on Multi-Attribute Decision-Making Methods Omid Bozorg-Haddad UniversityofTehran Alborz,Iran Babak Zolghadr-Asli UniversityofTehran (cid:2) (cid:2) Alborz,Iran Hugo A. Loáiciga UniversityofCalifornia SantaBarbara,UnitedStates (cid:2) (cid:2) Thiseditionfirstpublished2021 ©2021JohnWileyandSons,Inc. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,or transmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise, exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleis availableathttp://www.wiley.com/go/permissions. TherightofOmidBozorg-Haddad,BabakZolghadr-Asli,andHugoA.Loáicigatobeidentifiedasthe authorsofthisworkhasbeenassertedinaccordancewithlaw. RegisteredOffice JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,USA EditorialOffice 111RiverStreet,Hoboken,NJ07030,USA Fordetailsofourglobaleditorialoffices,customerservices,andmoreinformationaboutWileyproducts visitusatwww.wiley.com. Wileyalsopublishesitsbooksinavarietyofelectronicformatsandbyprint-on-demand.Somecontent thatappearsinstandardprintversionsofthisbookmaynotbeavailableinotherformats. 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LibraryofCongressCataloging-in-PublicationData Names:Bozorg-Haddad,Omid,1974-author.|Zolghadr-Asli,Babak,author.| Loáiciga,HugoA.,author. Title:Ahandbookonmulti-attributedecision-makingmethods/Omid Bozorg-Haddad,BabakZolghadr-Asli,HugoA.Loáiciga. Description:Hoboken,NJ:Wiley,2021.|Series:Wileyseriesin operationsresearchandmanagementscience|Includesbibliographical referencesandindex. Identifiers:LCCN2020034049(print)|LCCN2020034050(ebook)|ISBN 9781119563495(cloth)|ISBN9781119563471(adobepdf)|ISBN 9781119563389(epub)|ISBN9781119563501(obook) Subjects:LCSH:Multiplecriteriadecisionmaking. Classification:LCCT57.95.B692021(print)|LCCT57.95(ebook)|DDC 658.4/03–dc23 LCrecordavailableathttps://lccn.loc.gov/2020034049 LCebookrecordavailableathttps://lccn.loc.gov/2020034050 CoverDesign:Wiley CoverImage:©connel/Shutterstock Setin9.5/12.5ptSTIXTwoTextbySPiGlobal,Chennai,India 10 9 8 7 6 5 4 3 2 1 (cid:2) (cid:2) vii Contents Preface xiii 1 AnOverviewoftheArtofDecision-making 1 1.1 Introduction 1 1.2 ClassificationofMADMMethods 5 1.2.1 PreferenceEvaluationMechanism 5 1.2.2 Attributes’Interactions 7 (cid:2) 1.2.3 TheMathematicalNatureofAttributes’Values 8 (cid:2) 1.2.3.1 DeterministicVs.Nondeterministic 8 1.2.3.2 FuzzyVs.Crisp 8 1.2.4 NumberofInvolvedDecision-makers 8 1.3 BriefChronicleofMADMMethods 9 1.4 Conclusion 10 References 12 2 SimpleWeightingMethods:WeightedSumandWeighted ProductMethods 17 2.1 Introduction 17 2.2 TheWeightedSumMethod 20 2.2.1 Step1:DefiningtheDecision-makingProblem 20 2.2.2 Step2:NormalizingtheElementsoftheDecision-matrix 21 2.2.3 Step3:AggregatingthePreferenceofAlternatives 21 2.3 TheWeightedProductMethod 21 2.4 Conclusion 22 References 22 3 AnalyticHierarchyProcess(AHP) 25 3.1 Introduction 25 3.2 TheHierarchicalStructure 27 (cid:2) (cid:2) viii Contents 3.3 ThePairwiseComparison 30 3.4 Inconsistency 33 3.5 QuadrupleAxiomsoftheAHP 35 3.6 StepwiseDescriptionoftheAHPMethod 36 3.6.1 Step1:DefiningtheDecision-makingProblem 36 3.6.2 Step2:PerformingthePairwiseComparisonThroughtheHierarchical Structure 37 3.6.3 Step3:EstimatingthePreferenceValueVectors 37 3.6.4 Step4:SynthesizingandComputingtheOverallPreferenceValueof Alternatives 38 3.6.5 Step5:EvaluatingtheResults’RationalityandSelectingtheBest Alternative 38 3.7 Conclusion 39 References 39 4 AnalyticNetworkProcess(ANP) 43 4.1 Introduction 43 4.2 NetworkVs.HierarchyStructure 45 4.3 StepwiseInstructiontotheANPMethod 48 4.3.1 Step1:DefiningtheDecision-makingProblem 48 (cid:2) (cid:2) 4.3.2 Step2:ConductingaPairwiseComparisonoftheElementsofthe Decision-makingProblem 49 4.3.3 Step3:FormingtheSupermatrix 52 4.3.4 Step4:ComputingtheWeightedSupermatrix 53 4.3.5 Step5:ComputingtheGlobalPriorityVectorsandChoosingtheMost SuitableAlternative 53 4.4 Conclusion 54 References 54 5 TheBest–WorstMethod(BWM) 59 5.1 Introduction 59 5.2 BasicPrinciplesoftheBWM 62 5.3 StepwiseDescriptionoftheBWM 63 5.3.1 Step1:DefiningtheDecision-MakingProblem 64 5.3.2 Step2:DeterminingtheReferenceCriteria 64 5.3.3 Step3:PairwiseComparisons 64 5.3.4 Step4:ComputingtheOptimalWeights 65 5.3.5 Step5:MeasuringtheInconsistencyofDecision-Makers Judgments 66 5.4 Conclusion 67 References 67 (cid:2) (cid:2) Contents ix 6 TOPSIS 71 6.1 Introduction 71 6.2 StepwiseDescriptionoftheTOPSISMethod 72 6.2.1 Step1:EstablishingtheFormationoftheDecision-making Problem 73 6.2.2 Step2:NormalizingtheElementoftheDecision-matrix 73 6.2.3 Step3:ComputingtheWeightedNormalizedPreferenceValues 74 6.2.4 Step4:DefiningtheReferenceAlternatives 74 6.2.5 Step5:CalculationoftheSeparationMeasure 75 6.2.6 Step6:ComputingtheRelativeClosenesstotheIdealSolution 76 6.2.7 Step7:RankingtheAlternatives 76 6.3 ACommonMisinterpretationofTOPSISResults 76 6.4 Conclusion 77 References 78 7 VIKOR 81 7.1 Introduction 81 7.2 StepwiseDescriptionoftheVIKORMethod 84 7.2.1 Step1:ModelingtheDecision-MakingProblem 84 7.2.2 Step2:NormalizingtheElementoftheDecision-Matrix 85 (cid:2) (cid:2) 7.2.3 Step3:Computethe“GroupSatisfaction”and“IndividualRegret” Parameters 85 7.2.4 Step4:ComputingtheVIKORParameter 86 7.2.5 Step5:RankingtheAlternatives 86 7.2.6 Step6:DeterminingtheCompromiseSolution 86 7.3 Conclusion 87 References 88 8 ELECTRE 91 8.1 Introduction 91 8.2 ABriefHistoryoftheELECTREFamilyofMethods 93 8.3 ELECTREI 94 8.4 ELECTREII 96 8.5 ELECTREIII 99 8.6 ELECTREIV 104 8.7 Conclusion 105 References 106 9 PROMETHEE 111 9.1 Introduction 111 9.2 CommonGroundofthePROMETHEEFamily 112 (cid:2) (cid:2) x Contents 9.2.1 Stage1:ConstructionoftheGeneralizedCriteria 113 9.2.2 Stage2:MappingtheOutrankRelationontheSetofFeasible Alternatives 116 9.2.3 Stage3:EvaluationtheRelationAmongtheFeasibleAlternatives 116 9.3 PROMETHEEI 117 9.4 PROMETHEEII 118 9.5 PROMETHEEIII 119 9.6 PROMETHEEIV 120 9.7 Conclusion 121 References 121 10 SuperiorityandInferiorityRanking(SIR) 125 10.1 Introduction 125 10.2 FoundationalBasesoftheSIRMethod 126 10.3 StepwiseDescriptionoftheSIRMethod 129 10.3.1 Step1:EstablishingtheFormationoftheDecision-Making Problem 129 10.3.2 Step2:ComputingtheSuperiorityandInferiorityScores 129 10.3.3 Step3:FormingtheSuperiorityandInferiorityMatrices 132 10.3.4 Step4:SuperiorityandInferiorityFlows 133 (cid:2) (cid:2) 10.3.5 Step5:RankingtheSetofFeasibleAlternatives 135 10.4 Conclusion 136 References 137 11 PAPRIKA 139 11.1 Introduction 139 11.2 StepwiseDescriptionofPAPRIKA 140 11.2.1 Step1:DefiningtheDecision-MakingProblem 141 11.2.2 Step2:IdentifyingtheNondominatedPairsofAlternative 141 11.2.3 Step3:RankingthePairsofNondominatedSolutions 142 11.2.4 Step4:CalculatingtheCompleteRankingofAlternatives 144 11.3 Conclusion 145 References 146 12 GrayRelationalAnalysis 149 12.1 Introduction 149 12.2 GraySystemTheory:TheFoundationandBasicPrinciples 150 12.3 GrayRelationalModeling 151 12.4 GrayTheoryinRelationtoMADM 153 12.5 Conclusion 155 References 155 (cid:2) (cid:2) Contents xi A WeightAssignmentApproaches 159 A.1 SubjectiveApproach:WeightedLeastSquares 160 A.2 ObjectiveApproach:MultiobjectiveProgrammingModel 162 References 164 B ABenchmarkExampleandaComparisonbetweenObjective-and Subjective-BasedMADMMethods 167 References 171 Index 173 (cid:2) (cid:2) (cid:2)