New Methods and Applications in Multiple Attribute Decision Making (MADM) (eBook)

Contents 6
Preface 14
About the Authors 16
Introduction 17
1 SMART Method 23
1.1 Introduction 23
1.2 Description of SMART Method 24
1.2.1 Rating the Attributes 24
1.2.2 The Effective Weights of Alternatives 24
1.2.3 The Normalized Weights 25
1.2.4 The Final Ranking of Alternatives 25
1.3 Case Study 26
1.4 Conclusion 28
2 REGIME Method 30
2.1 Introduction 30
2.2 Description of REGIME Method 31
2.2.1 Superiority Index 31
2.2.2 Superiority Identifier 31
2.2.3 Impacts Matrix 31
2.2.4 REGIME Matrix 31
2.2.5 The Guide Index 32
2.2.6 The Final Ranking of Alternatives 32
2.3 Case Study 32
2.4 Conclusion 35
3 ORESTE Method 37
3.1 Introduction 37
3.2 Description of ORESTE Method 38
3.2.1 The Position Matrix 38
3.2.2 The Block Distance 38
3.2.3 The Block Distance Matrix 38
3.2.4 The Final Ranking of Alternatives 38
3.3 Case Study 39
3.4 Conclusion 41
4 VIKOR Method 42
4.1 Introduction 42
4.2 Description of LP-Metric 43
4.3 Description of VIKOR Method 43
4.3.1 The {/varvec f}^{*} and {/varvec f}^{ - } Indexes 43
4.3.2 The {/varvec S}_{ } and {/varvec R}_{ } Indexes 44
4.3.3 The VIKOR Index 44
4.3.4 The Final Ranking of Alternatives 44
4.4 Case Study 44
4.5 Conclusion 46
5 PROMETHEE I-II-III Methods 47
5.1 Introduction 47
5.2 Description of PROMETHEE Methods 48
5.2.1 The Preference Function 48
5.2.2 The Preference Index 50
5.2.3 The Leaving and Entering Flows 50
5.2.4 The Net Flow 50
5.2.5 Final Ranking of Alternatives (PROMETHEE I Method) 51
5.2.6 Final Ranking of Alternatives (PROMETHEE II Method) 51
5.2.7 Final Ranking of Alternatives (PROMETHEE III Method) 52
5.3 Case Study 52
5.4 Conclusion 56
6 QUALIFLEX Method 58
6.1 Introduction 58
6.2 Description of QUALIFLEX Method 59
6.2.1 The Initial Permutation of Alternatives 59
6.2.2 The Initial Ranking of Alternatives 59
6.2.3 The Dominant and Dominated Values 59
6.2.4 The Permutation Values of Attributes 60
6.2.5 The Permutation Values of Alternatives 60
6.2.6 The Final Ranking of Alternatives 60
6.3 Case Study 60
6.4 Conclusion 63
7 SIR Method 64
7.1 Introduction 64
7.2 Description of SIR Method 65
7.2.1 Comparing the Alternatives 65
7.2.2 The Preference Function 65
7.2.3 The (S) and (I) Indexes and (S) and (I) Matrices 67
7.2.4 The Flow Matrix 68
7.2.5 The (n) and (r) Flows 68
7.2.6 Final Ranking of Alternatives (SIR-SAW Method) 69
7.2.7 Final Ranking of Alternatives (SIR-PROMETHEE I Method) 69
7.2.8 Final Ranking of Alternatives (SIR-PROMETHEE II Method) 69
7.3 Case Study 69
7.4 Conclusion 75
8 EVAMIX Method 76
8.1 Introduction 76
8.2 Description of EVAMIX Method 77
8.2.1 The Superiority Rate of Alternatives 77
8.2.1.1 The First Technique for Calculating Weights 77
8.2.1.2 The Second Technique for Calculating Weights 77
8.2.2 The Differential Matrix in the Ordinal Attributes 78
8.2.3 The Differential Matrix in the Cardinal Attributes 78
8.2.4 The Total Dominance 78
8.2.5 The Final Ranking of Alternatives 79
8.3 Case Study 79
8.4 Conclusion 82
9 ARAS Method 83
9.1 Introduction 83
9.2 Description of ARAS Method 84
9.2.1 The Normalized Decision Matrix 84
9.2.2 The Weighted Normalized Decision Matrix 84
9.2.3 The Optimality Function 84
9.2.4 The Utility Degree 85
9.2.5 The Final Ranking of Alternatives 85
9.3 Case Study 85
9.4 Conclusion 87
10 Taxonomy Method 88
10.1 Introduction 88
10.2 Description of Taxonomy Method 89
10.2.1 The Mean and Standard Deviation of Attributes 89
10.2.2 The Standard Matrix 89
10.2.3 The Composite Distance Matrix 89
10.2.4 Homogenizing the Alternatives 90
10.2.5 The Development Pattern 91
10.2.6 The Final Ranking of Alternatives 91
10.3 Case Study 91
10.4 Conclusion 94
11 MOORA Method 95
11.1 Introduction 95
11.2 Description of MOORA Method 96
11.2.1 The Normalized Decision Matrix 96
11.2.2 The Reference Points 96
11.2.3 The Assessment Values 96
11.2.4 The Final Ranking of Alternatives 96
11.3 Case Study 97
11.4 Conclusion 99
12 COPRAS Method 100
12.1 Introduction 100
12.2 Description of COPRAS Method 101
12.2.1 The Normalized Decision Matrix 101
12.2.2 The Weighted Normalized Decision Matrix 101
12.2.3 The Maximizing and Minimizing Indexes 101
12.2.4 The Relative Significance Value 102
12.2.5 The Final Ranking of Alternatives 102
12.3 Case Study 102
12.4 Conclusion 104
13 WASPAS Method 105
13.1 Introduction 105
13.2 Description of WASPAS Method 106
13.2.1 The Normalized Decision Matrix 106
13.2.2 The Additive Relative Importance 106
13.2.3 The Multiplicative Relative Importance 106
13.2.4 The Joint Generalized Criterion (Q) 107
13.2.5 The Final Ranking of Alternatives 107
13.3 Case Study 107
13.4 Conclusion 110
14 SWARA Method 111
14.1 Introduction 111
14.2 Description of SWARA Method 111
14.2.1 The Initial Prioritization of Attributes 111
14.2.2 The Coefficient (K) 112
14.2.3 The Initial Weight 112
14.2.4 The Relative Weight 112
14.2.5 The Final Ranking of Attributes 112
14.3 Case Study 112
14.4 Conclusion 114
15 DEMATEL Method 115
15.1 Introduction 115
15.2 Description of DEMATEL Method 116
15.2.1 The Normalized Direct Relation Matrix 116
15.2.2 The Total Relation Matrix 116
15.2.3 The Cause and Effect Values 116
15.2.4 The Threshold Value (a) 117
15.2.5 The Interrelationship Map 117
15.2.6 The Final Ranking of Attributes 117
15.3 Case Study 118
15.4 Conclusion 120
16 MACBETH Method 121
16.1 Introduction 121
16.2 Description of MACBETH Method 122
16.2.1 Converting of Semantic Scale into Numerical Scale 122
16.2.2 The Reference Levels 122
16.2.3 The MACBETH Score (V) 122
16.2.4 The Overall Score 123
16.2.5 The Final Ranking of Alternatives 123
16.3 Case Study 123
16.4 Conclusion 125
17 ANP Method 127
17.1 Introduction 127
17.2 Description of ANP Method 128
17.2.1 The Priority Vectors 128
17.2.2 The Super Matrix 129
17.2.3 The Cluster Matrix 129
17.2.4 The Weighted Super Matrix 129
17.2.5 The Limit Super Matrix 129
17.2.6 The Utility Index 130
17.2.7 The Final Ranking of Alternatives 130
17.3 Case Study 130
17.4 Conclusion 136
18 MAUT Method 138
18.1 Introduction 138
18.2 Description of MAUT Method 139
18.2.1 The Normalized Decision Matrix 139
18.2.2 The Marginal Utility Score 139
18.2.3 The Final Utility Score 139
18.2.4 The Final Ranking of Alternatives 140
18.3 Case Study 140
18.4 Conclusion 142
19 IDOCRIW Method 143
19.1 Introduction 143
19.2 Description of IDOCRIW Method 144
19.2.1 The Normalized Decision Matrix 144
19.2.2 The Degree of Entropy 144
19.2.3 The Entropy Weight (W) 144
19.2.4 The Square Matrix 144
19.2.5 The Relative Impact Loss Matrix 145
19.2.6 The Weight System Matrix 145
19.2.7 The Criterion Impact Loss Weight (Q) 146
19.2.8 The Aggregate Weight (?) 146
19.2.9 The Final Ranking of Attributes 146
19.3 Case Study 146
19.4 Conclusion 150
20 TODIM Method 152
20.1 Introduction 152
20.2 Description of TODIM Method 153
20.2.1 The Normalized Decision Matrix 153
20.2.2 The Relative Weight 153
20.2.3 The Dominance Degree 153
20.2.4 The Overall Dominance Degree 154
20.2.5 The Final Ranking of Alternatives 154
20.3 Case Study 154
20.4 Conclusion 157
21 EDAS Method 158
21.1 Introduction 158
21.2 Description of EDAS Method 159
21.2.1 The Average Solution 159
21.2.2 The Positive and Negative Distances from Average Solution 159
21.2.3 The Weighted PDA and NDA 159
21.2.4 Weighted Normalized PDA and NDA 160
21.2.5 The Appraisal Score 160
21.2.6 The Final Ranking of Alternatives 160
21.3 Case Study 160
21.4 Conclusion 164
22 PAMSSEM I & II
22.1 Introduction 165
22.2 Description of PAMSSEM Methods 166
22.2.1 The Local Outranking Index 166
22.2.2 The Concordance Index 166
22.2.3 The Local Discordance Index 167
22.2.4 The Outranking Degree 167
22.2.5 The Entering and Leaving Flows 168
22.2.6 The Net Flow 168
22.2.7 The Final Ranking of Alternatives (PAMSSEM I Method) 168
22.2.8 The Final Ranking of Alternatives (PAMSSEM II Method) 168
22.3 Case Study 169
22.4 Conclusion 172
23 ELECTRE I–II–III Methods 174
23.1 Introduction 174
23.2 Description of ELECTRE Methods 175
23.2.1 The Normalized Decision Matrix 175
23.2.2 The Weighted Normalized Decision Matrix 175
23.2.3 The Dominant Matrix 175
23.2.4 The Dominated Matrix 175
23.2.5 The Concordance Matrix 176
23.2.6 The Discordance Matrix 176
23.2.7 The Aggregate Dominant Matrix 177
23.2.8 The Final Ranking of Alternatives (ELECTRE I Method) 177
23.2.9 The Final Ranking of Alternatives (ELECTRE II Method) 177
23.2.10 The Final Ranking of Alternatives (ELECTRE III Method) 178
23.3 Case Study 179
23.4 Conclusion 186
24 EXPROM I & II Method
24.1 Introduction 188
24.2 Description of EXPROM Methods 189
24.2.1 The Weak Preference Function 189
24.2.2 The Weak Preference Index 189
24.2.3 The Strict Preference Function 191
24.2.4 The Strict Preference Index 192
24.2.5 The Entering and Leaving Flows 192
24.2.6 The Net Flow 192
24.2.7 The Final Ranking of Alternatives (EXPROM I Method) 193
24.2.8 The Final Ranking of Alternatives (EXPROM II Method) 193
24.3 Case Study 194
24.4 Conclusion 198
25 MABAC Method 199
25.1 Introduction 199
25.2 Description of MABAC Method 200
25.2.1 The Normalized Decision Matrix 200
25.2.2 The Weighted Normalized Decision Matrix 200
25.2.3 The Border Approximation Area Matrix 200
25.2.4 The Distance from the Border Approximation Area 201
25.2.5 The Total Distances from the Border Approximate Area 201
25.2.6 The Final Ranking of Alternatives 201
25.3 Case Study 201
25.4 Conclusion 203
26 CRITIC Method 205
26.1 Introduction 205
26.2 Description of CRITIC Method 206
26.2.1 The Normalized Decision Matrix 206
26.2.2 The Correlation Coefficient 206
26.2.3 The Index (C) 206
26.2.4 The Weight of Attributes 207
26.2.5 The Final Ranking of Attributes 207
26.3 Case Study 207
26.4 Conclusion 209
27 KEMIRA Method 210
27.1 Introduction 210
27.2 Description of KEMIRA Method 211
27.2.1 The Normalized Decision Matrix 211
27.2.2 The Median Matrix 211
27.2.3 The Set of Attribute Weights 212
27.2.4 The Final Weight of Attributes 212
27.2.5 The Final Value of Alternatives 212
27.2.6 The Final Ranking of Alternatives 213
27.3 Case Study 213
27.4 Conclusion 220
References 221
Index 234