Table Of Content(cid:2)
AHandbookonMulti-AttributeDecision-MakingMethods
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A Handbook on Multi-Attribute
Decision-Making Methods
Omid Bozorg-Haddad
UniversityofTehran
Alborz,Iran
Babak Zolghadr-Asli
UniversityofTehran
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Alborz,Iran
Hugo A. Loáiciga
UniversityofCalifornia
SantaBarbara,UnitedStates
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Thiseditionfirstpublished2021
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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
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9781119563495(cloth)|ISBN9781119563471(adobepdf)|ISBN
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Subjects:LCSH:Multiplecriteriadecisionmaking.
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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
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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
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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
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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
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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
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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
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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
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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
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