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
DESCRIPTION Clear and effective instruction on MADM methods for students, researchers, and practitioners.
A Handbook on Multi-Attribute Decision-Making Methods describes multi-attribute decision-making (MADM) methods and provides step-by-step guidelines for applying them. The authors describe the most important MADM methods and provide an assessment of their performance in solving problems across disciplines. After offering an overview of decision-making and its fundamental concepts, this book covers 20 leading MADM methods and contains an appendix on weight assignment methods. Chapters are arranged with optimal learning in mind, so you can easily engage with the content found in each chapter. Dedicated readers may go through the entire book to gain a deep understanding of MADM methods and their theoretical foundation, and others may choose to review only specific chapters. Each standalone chapter contains a brief description of prerequisite materials, methods, and mathematical concepts needed to cover its content, so you will not face any difficulty understanding single chapters. Each chapter:
Describes, step-by-step, a specific MADM method, or in some cases a family of methods Contains a thorough literature review for each MADM method, supported with numerous examples of the method's implementation in various fields Provides a detailed yet concise description of each method's theoretical foundation Maps each method's philosophical basis to its corresponding mathematical framework Demonstrates how to implement each MADM method to real-world problems in a variety of disciplines In MADM methods, stakeholders' objectives are expressible through a set of often conflicting criteria, making this family of decision-making approaches relevant to a wide range of situations. A Handbook on Multi-Attribute Decision-Making Methods compiles and explains the most important methodologies in a clear and systematic manner, perfect for students and professionals whose work involves operations research and decision making.