Preface xiii
1 An Overview of the Art of Decision-making 1
1.1 Introduction 1
1.2 Classification of MADM Methods 5
1.2.1 Preference Evaluation Mechanism 5
1.2.2 Attributes’ Interactions 7
1.2.3 The Mathematical Nature of Attributes’ Values 8
1.2.3.1 Deterministic Vs. Nondeterministic 8
1.2.3.2 Fuzzy Vs. Crisp 8
1.2.4 Number of Involved Decision-makers 8
1.3 Brief Chronicle of MADM Methods 9
1.4 Conclusion 10
References 12
2 Simple Weighting Methods: Weighted Sum and Weighted Product Methods 17
2.1 Introduction 17
2.2 The Weighted Sum Method 20
2.2.1 Step 1: Defining the Decision-making Problem 20
2.2.2 Step 2: Normalizing the Elements of the Decision-matrix 21
2.2.3 Step 3: Aggregating the Preference of Alternatives 21
2.3 The Weighted Product Method 21
2.4 Conclusion 22
References 22
3 Analytic Hierarchy Process (AHP) 25
3.1 Introduction 25
3.2 The Hierarchical Structure 27
3.3 The Pairwise Comparison 30
3.4 Inconsistency 33
3.5 Quadruple Axioms of the AHP 35
3.6 Stepwise Description of the AHP Method 36
3.6.1 Step 1: Defining the Decision-making Problem 36
3.6.2 Step 2: Performing the Pairwise Comparison Through the Hierarchical Structure 37
3.6.3 Step 3: Estimating the Preference Value Vectors 37
3.6.4 Step 4: Synthesizing and Computing the Overall Preference Value of Alternatives 38
3.6.5 Step 5: Evaluating the Results’ Rationality and Selecting the Best Alternative 38
3.7 Conclusion 39
References 39
4 Analytic Network Process (ANP) 43
4.1 Introduction 43
4.2 Network Vs. Hierarchy Structure 45
4.3 Stepwise Instruction to the ANP Method 48
4.3.1 Step 1: Defining the Decision-making Problem 48
4.3.2 Step 2: Conducting a Pairwise Comparison of the Elements of the Decision-making Problem 49
4.3.3 Step 3: Forming the Supermatrix 52
4.3.4 Step 4: Computing the Weighted Supermatrix 53
4.3.5 Step 5: Computing the Global Priority Vectors and Choosing the Most Suitable Alternative 53
4.4 Conclusion 54
References 54
5 The Best–Worst Method (BWM) 59
5.1 Introduction 59
5.2 Basic Principles of the BWM 62
5.3 Stepwise Description of the BWM 63
5.3.1 Step 1: Defining the Decision-Making Problem 64
5.3.2 Step 2: Determining the Reference Criteria 64
5.3.3 Step 3: Pairwise Comparisons 64
5.3.4 Step 4: Computing the Optimal Weights 65
5.3.5 Step 5: Measuring the Inconsistency of Decision-Makers Judgments 66
5.4 Conclusion 67
References 67
6 TOPSIS 71
6.1 Introduction 71
6.2 Stepwise Description of the TOPSIS Method 72
6.2.1 Step 1: Establishing the Formation of the Decision-making Problem 73
6.2.2 Step 2: Normalizing the Element of the Decision-matrix 73
6.2.3 Step 3: Computing theWeighted Normalized Preference Values 74
6.2.4 Step 4: Defining the Reference Alternatives 74
6.2.5 Step 5: Calculation of the Separation Measure 75
6.2.6 Step 6: Computing the Relative Closeness to the Ideal Solution 76
6.2.7 Step 7: Ranking the Alternatives 76
6.3 A Common Misinterpretation of TOPSIS Results 76
6.4 Conclusion 77
References 78
7 VIKOR 81
7.1 Introduction 81
7.2 Stepwise Description of the VIKOR Method 84
7.2.1 Step 1: Modeling the Decision-Making Problem 84
7.2.2 Step 2: Normalizing the Element of the Decision-Matrix 85
7.2.3 Step 3: Compute the “Group Satisfaction” and “Individual Regret” Parameters 85
7.2.4 Step 4: Computing the VIKOR Parameter 86
7.2.5 Step 5: Ranking the Alternatives 86
7.2.6 Step 6: Determining the Compromise Solution 86
7.3 Conclusion 87
References 88
8 ELECTRE 91
8.1 Introduction 91
8.2 A Brief History of the ELECTRE Family of Methods 93
8.3 ELECTRE I 94
8.4 ELECTRE II 96
8.5 ELECTRE III 99
8.6 ELECTRE IV 104
8.7 Conclusion 105
References 106
9 PROMETHEE 111
9.1 Introduction 111
9.2 Common Ground of the PROMETHEE Family 112
9.2.1 Stage 1: Construction of the Generalized Criteria 113
9.2.2 Stage 2: Mapping the Outrank Relation on the Set of Feasible Alternatives 116
9.2.3 Stage 3: Evaluation the Relation Among the Feasible Alternatives 116
9.3 PROMETHEE I 117
9.4 PROMETHEE II 118
9.5 PROMETHEE III 119
9.6 PROMETHEE IV 120
9.7 Conclusion 121
References 121
10 Superiority and Inferiority Ranking (SIR) 125
10.1 Introduction 125
10.2 Foundational Bases of the SIR Method 126
10.3 Stepwise Description of the SIR Method 129
10.3.1 Step 1: Establishing the Formation of the Decision-Making Problem 129
10.3.2 Step 2: Computing the Superiority and Inferiority Scores 129
10.3.3 Step 3: Forming the Superiority and Inferiority Matrices 132
10.3.4 Step 4: Superiority and Inferiority Flows 133
10.3.5 Step 5: Ranking the Set of Feasible Alternatives 135
10.4 Conclusion 136
References 137
11 PAPRIKA 139
11.1 Introduction 139
11.2 Stepwise Description of PAPRIKA 140
11.2.1 Step 1: Defining the Decision-Making Problem 141
11.2.2 Step 2: Identifying the Nondominated Pairs of Alternative 141
11.2.3 Step 3: Ranking the Pairs of Nondominated Solutions 142
11.2.4 Step 4: Calculating the Complete Ranking of Alternatives 144
11.3 Conclusion 145
References 146
12 Gray Relational Analysis 149
12.1 Introduction 149
12.2 Gray System Theory: The Foundation and Basic Principles 150
12.3 Gray Relational Modeling 151
12.4 Gray Theory in Relation to MADM 153
12.5 Conclusion 155
References 155
A Weight Assignment Approaches 159
A.1 Subjective Approach: Weighted Least Squares 160
A.2 Objective Approach: Multiobjective Programming Model 162
References 164
B A Benchmark Example and a Comparison between Objective- and Subjective-Based MADM Methods 167
References 171
Index 173
