Multi-criteria decision making methods: a comparative study
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2000
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| Series: | Applied optimization
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVIII, 288 S. graph. Darst. |
| ISBN: | 0792366077 |
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| 100 | 1 | |a Triantaphyllou, Evangelos |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multi-criteria decision making methods |b a comparative study |c by Evangelos Triantaphyllou |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 2000 | |
| 300 | |a XXVIII, 288 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Applied optimization |v 44 | |
| 650 | 4 | |a Multiple criteria decision making | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
List of Figures xiii
List of Tables xix
Foreword xxiii
Preface xcv
Acknowledgments xxix
1 Introduction to Multi Criteria Decision Making 1
1.1 Multi Criteria Decision Making:
A General Overview 1
1.2 Classification of MCDM Methods 3
2 Multi Criteria Decision Making Methods 5
2.1 Background Information 5
2.2 Description of Some MCDM Methods 5
2.2.1 The WSM Method 6
2.2.2 The WPM Method 8
2.2.3 The AHP Method 9
2.2.4 The Revised AHP Method 11
2.2.5 The ELECTRE Method 13
2.2.6 The TOPSIS Method 18
3 Quantification of Qualitative Data for
MCDM Problems 23
3.1 Background Information 23
3.2 Scales for Quantifying Pairwise Comparisons 25
3.2.1 Scales Defined on the Interval [9, 1/9] 26
3.2.2 Exponential Scales 28
3.2.3 Some Examples of the Use of
Exponential Scales 29
3.3 Evaluating Different Scales 32
3.3.1 The Concepts of the RCP and CDP Matrices . . 32
3.3.2 On The Consistency of CDP Matrices 35
3.3.3 Two Evaluative Criteria 43
3.4 A Simulation Evaluation of Different Scales 44
3.5 Analysis of the Computational Results 50
3.6 Conclusions 53
viii MCDM Methods: A Comparative Study, by E. Triantaphyllou
4 Deriving Relative Weights from Ratio Comparisons 57
4.1 Background Information 57
4.2 The Eigenvalue Approach 58
4.3 Some Optimization Approaches 60
4.4 Considering The Human Rationality Factor 61
4.5 First Extensive Numerical Example 65
4.6 Second Extensive Numerical Example 66
4.7 Average Error per Comparison for Sets
of Different Size 67
4.8 Conclusions 72
5 Deriving Relative Weights from Difference Comparisons ... 73
5.1 Background Information 73
5.2 Pairwise Comparisons of Relative Similarity 76
5.2.1 Quantifying Pairwise Comparisons
of Relative Similarity 76
5.2.2 Processing Pairwise Comparisons
of Relative Similarity 77
5.2.3 An Extensive Numerical Example 79
5.3 Conclusions 85
6 A Decomposition Approach for Evaluating Relative
Weights Derived from Comparisons 87
6.1 Background Information 87
6.2 Problem Description 88
6.3 Two Solution Approaches 91
6.3.1 A Simple Approach 91
6.3.2 A Linear Programming Approach 92
6.4 An Extensive Numerical Example 95
6.5 Some Computational Experiments 97
6.6 Analysis of the Computational Results 100
6.7 Conclusions 112
7 Reduction of Pairwise Comparisons Via a
Duality Approach 115
7.1 Background Information 115
7.2 A Duality Approach for Eliciting Comparisons 116
7.3 An Extensive Numerical Example 120
7.3.1 Applying the Primal Approach 121
Table of Contents jx
7.3.2 Applying the Dual Approach 122
7.4 Some Numerical Results for Problems of
Different Sizes 124
7.5 Conclusions 128
8 A Sensitivity Analysis Approach for MCDM Methods .... 131
8.1 Background Information 131
8.2 Description of the Two Major Sensitivity
Analysis Problems 133
8.3. Problem 1: Determining the Most Critical
Criterion 135
8.3.1 Definitions and Terminology 135
8.3.2 Some Theoretical Results in Determining
the Most Critical Criterion 137
8.3.2.1 Case (/): Using the WSM or the
AHP Method 137
8.3.2.2 An Extensive Numerical Example
for the WSM Case 138
8.3.2.3 Case (ii): Using the WPM Method . . 142
8.3.2.4 An Extensive Numerical Example
for the WPM Case 143
8.3.3 Some Computational Experiments 145
8.4 Problem 2: Determining the Most Critical a^
Measure of Performance 155
8.4.1 Definitions and Terminology 155
8.4.2 Determining the Threshold
Values r Uik 157
8.4.2.1 Case (/): When Using the WSM
or the AHP Method 157
8.4.2.2 An Extensive Numerical Example
When the WSM or the
AHP Method is Used 158
8.4.2.3 Case (ii): When Using the WPM
Method 161
8.4.2.4 An Extensive Numerical Example
When the WPM Method is Used .... 161
8.5 Conclusions 165
X MCDM Methods: A Comparative Study, by E. Triantaphyllou
Appendix to Chapter 8 167
8.6 Calculation of the 5,, 2 Quantity When
the AHP or the WSM Method is Used 167
8.7 Calculation of the 5Mt2 Quantity When
the WPM Method is Used 169
8.8 Calculation of the r345 Quantity When
the WSM Method is Used 170
8.9 Calculation of the r345 Quantity When
the AHP Method is Used 171
8.10 Calculation of the t3 4 5 Quantity When
the WPM Method is Used 174
9 Evaluation of Methods for Processing a
Decision Matrix and Some Cases
of Ranking Abnormalities 177
9.1 Background Information 177
9.2 Two Evaluative Criteria 177
9.3 Testing the Methods by Using the First
Evaluative Criterion 179
9.4 Testing the Methods by Using the Second
Evaluative Criterion 186
9.5 Analysis of the Computational Results 192
9.6 Evaluating the TOPSIS Method 194
9.7 Conclusions 197
10 A Computational Evaluation of the Original
and the Revised AHP 201
10.1 Background Information 201
10.2 An Extensive Numerical Example 202
10.3 Some Computational Experiments 206
10.4 Conclusions 212
11 More Cases of Ranking Abnormalities When Some
MCDM Methods Are Used 213
11.1 Background Information 213
11.2 Ranking Irregularities When Alternatives Are
Compared Two at a Time 215
11.3 Ranking Irregularities When Alternatives Are
Compared Two at a Time and Also as a Group 220
Table of Contents xj
11.4 Some Computational Results 223
11.5 A Multiplicative Version of the AHP 228
11.6 Results from Two Real Life Case Studies 230
11.6.1 Comparative Ranking Analysis of
the Bridge Evaluation Problem 230
11.6.2 Comparative Ranking Analysis of
the Site Selection Problem 232
11.7 Conclusions 233
12 Fuzzy Sets and Their Operations 235
12.1 Background Information 235
12.2 Fuzzy Operations 236
12.3 Ranking of Fuzzy Numbers 238
13 Fuzzy Multi Criteria Decision Making 241
13.1 Background Information 241
13.2 The Fuzzy WSM Method 242
13.3 The Fuzzy WPM Method 244
13.4 The Fuzzy AHP Method 245
13.5 The Fuzzy Revised AHP Method 247
13.6 The Fuzzy TOPSIS Method 248
13.7 Two Fuzzy Evaluative Criteria for
Fuzzy MCDM Methods 250
13.7.1 Testing the Methods by Using the First
Fuzzy Evaluative Criterion 251
13.7.2 Testing the Methods by Using the Second
Fuzzy Evaluative Criterion 255
13.8 Computational Experiments 257
13.8.1 Description of the Computational
Results 258
13.8.2 Analysis of the Computational
Results 261
13.9 Conclusions 262
14 Conclusions and Discussion for Future Research 263
14.1 The Study of MCDM Methods:
Future Trends 263
14.2 Lessons Learned 263
xii MCDM Methods: A Comparative Study, by E. Triantaphyllou
References 267
Subject Index 275
Author Index 283
About the Author 289
LIST OF FIGURES
1 Introduction to Multi Criteria Decision Making .... 1
Figure 1 1: A Typical Decision Matrix 3
Figure 1 2: A Taxonomy of MCDM methods (according to
Chen and Hwang [1991]) 4
2 Multi Criteria Decision Making Methods 5
3 Quantification of Qualitative Data for
MCDM Problems 23
Figure 3 1: Actual Comparison Values 37
Figure 3 2: Maximum, Average, and Minimum CI Values of
Random CDP Matrices When the Original
Saaty Scale is used 42
Figure 3 3: Inversion Rates for Different Scales and Size
of Set (Class 1 Scales) 46
Figure 3 4: Indiscrimination Rates for Different Scales
and Size of Set (Class 1 Scales) 47
Figure 3 5: Inversion Rates for Different Scales and Size
of Set (Class 2 Scales) 48
Figure 3 6: Indiscrimination Rates for Different Scales
and Size of Set (Class 2 Scales) 49
Figure 3 7: The Best Scales 51
Figure 3 8: The Worst Scales 52
4 Deriving Relative Weights from Ratio Comparisons . 57
Figure 4 1: Average Residual and CI versus Order of Set
When the Human Rationality Assumption is Used
(the Results Correspond to 100 Random Observations) . 70
Figure 4 2: Average Residual and CI versus Order of Set
When the Eigenvalue Method is Used
(the Results Correspond to 100 Random Observations) . 71
5 Deriving Relative Weights from Difference
Comparisons 73
xiv MCDM Methods: A Comparative Study, by E. TriantaphyUou
6 A Decomposition Approach for Evaluating Relative
Weights Derived from Comparisons 87
Figure 6 1: Partitioning of the n(n l)/2 Pairwise
Comparisons 90
Figure 6 2: Error Rates Under the LP Approach for Sets
of Different Size as a Function of the
Available Comparisons 106
Figure 6 3: Error Rates Under the Non LP Approach for Sets
of Different Size as a Function of the
Available Comparisons 107
Figure 6 4: Error Rates Under the LP Approach for Sets
of Different Size as a Function of the
Common Comparisons 108
Figure 6 5: Error Rates Under the Non LP Approach for Sets
of Different Size as a Function of the
Common Comparisons 109
Figure 6 6: Error Rates for the two Approaches as a
Function of the Available Comparisons 110
Figure 6 7: Error Rates for the two Approaches as a
Function of the Common Comparisons Ill
7 Reduction of Pairwise Comparisons Via a
Duality Approach 115
Figure 7 1: Total Number of Comparisons and Reduction
Achieved When the Dual Approach is Used.
The Number of Criteria n = 5 125
Figure 7 2: Total Number of Comparisons and Reduction
Achieved When the Dual Approach is Used.
The Number of Criteria n = 10 125
Figure 7 3: Total Number of Comparisons and Reduction
Achieved When the Dual Approach is Used.
The Number of Criteria n = 15 126
Figure 7 4: Total number of Comparisons and Reduction
Achieved When the Dual Approach is Used.
The Number of Criteria n = 20 126
Figure 7 5: Net Reduction on the Number of
Comparisons When the Dual Approach is used.
Results for Problems of Various Sizes 127
Figure 7 6: Percent (%) Reduction on the Number of
Comparisons When the Dual Approach is used.
Results for Problems of Various Sizes 127
List of Figures xv
8 A Sensitivity Analysis Approach
for MCDM Methods 131
Figure 8 1: Frequency of the time that the PT Critical
Criterion is the Criterion with
the Highest Weight 149
Figure 8 2: Frequency of the time that the PT Critical
Criterion is the Criterion with
the Lowest Weight 149
Figure 8 3: Frequency of the time that the PA Critical
Criterion is the Criterion with
the Highest Weight 150
Figure 8 4: Frequency of the time that the PA Critical
Criterion is the Criterion with
the Lowest Weight 150
Figure 8 5: Frequency of the time that the AT Critical
Criterion is the Criterion with
the Highest Weight 151
Figure 8 6: Frequency of the time that the AT Critical
Criterion is the Criterion with
the Lowest Weight 151
Figure 8 7: Frequency of the time that the AA Critical
Criterion is the Criterion with
the Highest Weight 152
Figure 8 8: Frequency of the time that the AA Critical
Criterion is the Criterion with
the Lowest Weight 152
Figure 8 9: Frequency of the time that the AT and PT
Definitions point to the Same Criterion 153
Figure 8 10: Frequency of the time that the A A and PA
Definitions point to the Same Criterion 153
Figure 8 11: Frequency of the time that the AT, PT, AA, and PA
Definitions point to the Same Criterion
Under the WSM Method 154
Figure 8 12: Rate that the AT Criterion is the one
with the Lowest Weight for Different Size
Problems Under the WPM Method 154
9 Evaluation of Methods for Processing a
Decision Matrix and Some Cases
of Ranking Abnormalities 177
Figure 9 1: Contradiction Rate (%) Between the
Xvi MCDM Methods: A Comparative Study, by E. Triantaphyllou
WSM and the AHP 184
Figure 9 2: Contradiction Rate (%) Between the
WSM and the Revised AHP 185
Figure 9 3: Contradiction Rate (%) Between the
WSM and the WPM 185
Figure 9 4: Rate of Change (%) of the Indication of the
Optimum Alternative When a Non Optimum
Alternative is Replaced by a Worse one.
The AHP Case 191
Figure 9 5: Rate of Change (%) of the indication of the
Optimum Alternative When a Non Optimum
Alternative is Replaced by a Worse one.
The Revised AHP Case 191
Figure 9 6: Contradiction Rate (%) Between the WSM
and TOPSIS Method 196
Figure 9 7: Rate of Change (%) of the Indication of the
Optimum Alternative When a Non Optimum
Alternative is Replaced by a Worse one.
The TOPSIS Case 196
Figure 9 8: Indication of the Best MCDM Method According
to Different MCDM Methods 198
10 A Computational Evaluation of the Original
and the Revised AHP 201
Figure 10 1: The Failure Rates are Based on 1,000 Randomly
Generated Problems. The AHP Case 210
Figure 10 2: The Failure Rates are Based on 1,000 Randomly
Generated Problems. The Revised AHP Case 211
11 More Cases of Ranking Abnormalities When Some
MCDM Methods Are Used 213
Figure 11 1: Contradiction Rates on the Indication of the
Best Alternative When Alternatives are
Considered Together and in Pairs.
The Original AHP Case 225
Figure 11 2: Contradiction Rates on the Indication of the
Best Alternative When Alternatives are
Considered Together and in Pairs.
The Ideal Mode (Revised) AHP Case 225
Figure 11 3: Contradiction Rates on the Indication of
List of Figures xvjj
Any Alternative When Alternatives are
Considered Together and in Pairs.
The Original AHP Case 226
Figure 11 4: Contradiction Rates on the Indication of
Any Alternative When Alternatives are
Considered Together and in Pairs.
The Ideal Mode (Revised) AHP Case 226
Figure 11 5: Contradiction Rates on the indication of
Any Alternative When Alternatives are
Considered in Pairs.
The Original AHP Case 227
Figure 11 6: Contradiction Rates on the indication of
Any Alternative When Alternatives are
Considered in Pairs.
The Ideal Mode AHP Case 227
12 Fuzzy Sets and Their Operations 235
Figure 12 1: Membership Functions for the Two Fuzzy
Alternatives A, and A2 239
13 Fuzzy Multi Criteria Decision Making 241
Figure 13 1: Membership Functions of the Fuzzy Alternatives
A,, A2, and A3 of Example 13 1 According
to the Fuzzy WSM Method 243
Figure 13 2: Membership Functions of the Fuzzy Alternatives
A,, A2, and A3 of Example 13 2 According
to the Fuzzy WPM Method 244
Figure 13 3: Contradiction Rate Rll When the Number of
Fuzzy Alternatives is Equal to 3 259
Figure 13 4: Contradiction Rate Rll When the Number of
Fuzzy Alternatives is Equal to 21 259
Figure 13 5: Contradiction Rate R21 When the Number of
Fuzzy Alternatives is Equal to 3 260
Figure 13 6: Contradiction Rate R21 When the Number of
Fuzzy Alternatives is Equal to 21 260
Figure 13 7: Contradiction Rate R12 When the Number of
Fuzzy Alternatives is Equal to 3 261
14 Conclusions and Discussion for Future Research . . 263
LIST OF TABLES
1 Introduction to Multi Criteria Decision Making .... 1
2 Multi Criteria Decision Making Methods 5
3 Quantification of Qualitative Data for
MCDM Problems 23
Table 3 1: Scale of Relative Importances
(according to Saaty[198O]) 27
Table 3 2: Scale of Relative Importances
(According to Lootsma[1988]) 28
Table 3 3: Two Exponential Scales 29
4 Deriving Relative Weights from Ratio
Comparisons 57
Table 4 1: RCI Values of Sets of Different Order n 59
Table 4 2: Data for the Second Extensive Numerical Example ... 66
Table 4 3: Comparison of the Weight Values for
the Data in Table 4 2 67
Table 4 4: Average Residual and CI Versus Order of Set and
CR When the Human Rationality Assumption (HR)
and the Eigenvalue Method (EM) is used.
Results Correspond to 100 Random Observations .... 69
5 Deriving Relative Weights from Difference
Comparisons 73
Table 5 1: Proposed Similarity Scale 77
6 A Decomposition Approach for Evaluating Relative
Weights Derived from Comparisons 87
Table 6 la: Computational Results, Part A 101
Table 6 lb: Computational Results, Part B 102
Table 6 lc: Computational Results, Part C 103
Table 6 ld: Computational Results, Part D 104
XX MCDM Methods: A Comparative Study, by E. Triantaphyllou
7 Reduction of Pairwise Comparisons Via a
Duality Approach 115
8 A Sensitivity Analysis Approach
for MCDM Methods 131
Table 8 1: Decision Matrix for the Numerical Example
on the WSM 139
Table 8 2: Current Final Preferences 139
Table 8 3: All Possible d^j Values (Absolute Change
in Criteria Weights) 140
Table 8 4: All Possible b kiJ Values (Percent Change
in Criteria Weights) 141
Table 8 5: Decision Matrix for the Numerical Example
on the WPM 143
Table 8 6: Current Ranking 144
Table 8 7: All Possible K Values for the WPM Example 145
Table 8 8: Decision Matrix and Initial Preferences for
the Example 158
Table 8 9: Threshold Values t JIc (%) in Relative
Terms for the WSM/AHP Example 159
Table 8 10: Criticality Degrees A ^ (%) for each ay
Performance Measure 160
Table 8 11: Sensitivity Coefficients sens{a^ for each av
Performance Measure 160
Table 8 12: Decision Matrix for Numerical Example 162
Table 8 13: Initial Ranking 162
Table 8 14: Threshold Values T iJk (%) in Relative
Terms for the WPM Example 163
Table 8 15: Criticality Degrees Ay (in %) for each a9
Measure of Performance 164
Table 8 16: Sensitivity Coefficients sensia^ for each a^
Measure of Performance 164
9 Evaluation of Methods for Processing a
Decision Matrix and Some Cases
of Ranking Abnormalities 177
Table 9 1: Contradiction Rate (%) Between the
WSM and the AHP 181
Table 9 2: Contradiction Rate (%) Between the
WSM and the Revised AHP 182
List of Tables xxj
Table 9 3: Contradiction Rate (%) Between the
WSM and the WPM 183
Table 9 4: Rate of Change (%) of the Indication of the
Optimum Alternative When a Non Optimum
Alternative is Replaced by a Worse One.
The AHP Case 188
Table 9 5: Rate of Change (%) of the Indication of the
Optimum Alternative When a Non Optimum
Alternative is Replaced by a Worse One.
The Case of the Revised AHP 188
Table 9 6: Summary of the Computational Results 190
Table 9 7: Contradiction Rate (%) Between the WSM and
the TOPSIS Method 194
Table 9 8: Rate of Change (%) of the Indication of the
Optimum Alternative When a Non Optimum
Alternative is Replaced by a Worse One.
The TOPSIS Case 195
10 A Computational Evaluation of the Original
and the Revised AHP 201
Table 10 1: The Failure Rates are Based on 1,000 Randomly
Generated Problems. The AHP Case 208
Table 10 2: The Failure Rates are Based on 1,000 Randomly
Generated Problems. The Revised AHP Case 209
11 More Ranking Abnormalities When Some
MCDM Methods Are Used 213
Table 11 1: Priorities and Rankings of the Alternatives in the
Bridge Evaluation Case Study [Saaty, 1994] 231
12 Fuzzy Sets and Their Operations 235
13 Fuzzy Multi Criteria Decision Making 241
14 Conclusions and Discussion for Future Research . . 263
|
| any_adam_object | 1 |
| author | Triantaphyllou, Evangelos |
| author_facet | Triantaphyllou, Evangelos |
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV013917870 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:22Z |
| institution | BVB |
| isbn | 0792366077 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009522523 |
| oclc_num | 247672854 |
| open_access_boolean | |
| owner | DE-703 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 |
| owner_facet | DE-703 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 |
| physical | XXVIII, 288 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| series | Applied optimization |
| series2 | Applied optimization |
| spelling | Triantaphyllou, Evangelos Verfasser aut Multi-criteria decision making methods a comparative study by Evangelos Triantaphyllou Dordrecht [u.a.] Kluwer 2000 XXVIII, 288 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 44 Multiple criteria decision making Multikriteria-Entscheidung (DE-588)4126083-1 gnd rswk-swf Entscheidungsfindung (DE-588)4113446-1 gnd rswk-swf Mehrfachoptimierung (DE-588)4604982-4 gnd rswk-swf Multikriteria-Entscheidung (DE-588)4126083-1 s DE-604 Entscheidungsfindung (DE-588)4113446-1 s Mehrfachoptimierung (DE-588)4604982-4 s Applied optimization 44 (DE-604)BV010841718 44 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009522523&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Triantaphyllou, Evangelos Multi-criteria decision making methods a comparative study Applied optimization Multiple criteria decision making Multikriteria-Entscheidung (DE-588)4126083-1 gnd Entscheidungsfindung (DE-588)4113446-1 gnd Mehrfachoptimierung (DE-588)4604982-4 gnd |
| subject_GND | (DE-588)4126083-1 (DE-588)4113446-1 (DE-588)4604982-4 |
| title | Multi-criteria decision making methods a comparative study |
| title_auth | Multi-criteria decision making methods a comparative study |
| title_exact_search | Multi-criteria decision making methods a comparative study |
| title_full | Multi-criteria decision making methods a comparative study by Evangelos Triantaphyllou |
| title_fullStr | Multi-criteria decision making methods a comparative study by Evangelos Triantaphyllou |
| title_full_unstemmed | Multi-criteria decision making methods a comparative study by Evangelos Triantaphyllou |
| title_short | Multi-criteria decision making methods |
| title_sort | multi criteria decision making methods a comparative study |
| title_sub | a comparative study |
| topic | Multiple criteria decision making Multikriteria-Entscheidung (DE-588)4126083-1 gnd Entscheidungsfindung (DE-588)4113446-1 gnd Mehrfachoptimierung (DE-588)4604982-4 gnd |
| topic_facet | Multiple criteria decision making Multikriteria-Entscheidung Entscheidungsfindung Mehrfachoptimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009522523&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010841718 |
| work_keys_str_mv | AT triantaphyllouevangelos multicriteriadecisionmakingmethodsacomparativestudy |