A handbook on multi-attribute decision-making methods

TABLE OF CONTENTS
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

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.