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