A Comparative Study, by Evangelos Triantaphyllou (original) (raw)
Multi-Criteria Decision Making Methods: A Comparative Study
by Evangelos Triantaphyllou, Ph.D.
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[1980])............................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 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 6-1a: Computational Results, Part A.......................101 Table 6-1b: Computational Results, Part B.......................102 Table 6-1c: Computational Results, Part C.......................103 Table 6-1d: Computational Results, Part D.......................104
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 deltak,i,j Values (Absolute Change in Criteria Weights).................................140 Table 8-4: All Possible delta/k,i,j 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 tau/i,j,k (%) in Relative Terms for the WSM/AHP Example........................159 Table 8-10: Criticality Degrees Delta /ij (%) for each aij Performance Measure..................................160 Table 8-11: Sensitivity Coefficients sens(aij) for each aij Performance Measure..................................160 Table 8-12: Decision Matrix for Numerical Example................162 Table 8-13: Initial Ranking......................................162 Table 8-14: Threshold Values tau/i,j,k (%) in Relative Terms for the WPM Example............................163 Table 8-15: Criticality Degrees Delta/ij (in %) for each aij Measure of Performance...............................164 Table 8-16: Sensitivity Coefficients sens(aij) for each aij 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
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
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