Multi-Criteria Decision Making Methods

by Triantaphyllou, Evangelos

• ISBN13: 9780792366072
• ISBN10: 0792366077
• Format: Hardcover
• Copyright: 2000-10-01
• Publisher: Kluwer Academic Pub

Summary

Multi-Criteria Decision Making (MCDM) has been one of the fastest growing problem areas in many disciplines. The central problem is how to evaluate a set of alternatives in terms of a number of criteria. Although this problem is very relevant in practice, there are few methods available and their quality is hard to determine. Thus, the question 'Which is the best method for a given problem?' has become one of the most important and challenging ones. This is exactly what this book has as its focus and why it is important. The author extensively compares, both theoretically and empirically, real-life MCDM issues and makes the reader aware of quite a number of surprising 'abnormalities' with some of these methods. What makes this book so valuable and different is that even though the analyses are rigorous, the results can be understood even by the non-specialist. Audience: Researchers, practitioners, and students; it can be used as a textbook for senior undergraduate or graduate courses in business and engineering.

Table of Contents

List of Figures	xiii
List of Tables	xix
Foreword	xxiii
Preface	xxv
Acknowledgments	xxix
Introduction to Multi-Criteria Decision Making	1	(4)
Multi-Criteria Decision Making: A General Overview	1	(2)
Classification of MCDM Methods	3	(2)
Multi-Criteria Decision Making Methods	5	(18)
Background Information	5	(1)
Description of Some MCDM Methods	5	(18)
The WSM Method	6	(2)
The WPM Method	8	(1)
The AHP Method	9	(2)
The Revised AHP Method	11	(2)
The ELECTRE Method	13	(5)
The TOPSIS Method	18	(5)
Quantification of Qualitative Data for MCDM Problems	23	(34)
Background Information	23	(2)
Scales for Quantifying Pairwise Comparisons	25	(7)
Scales Defined on the Interval [9, 1/9]	26	(2)
Exponential Scales	28	(1)
Some Examples of the Use of Exponential Scales	29	(3)
Evaluating Different Scales	32	(12)
The Concepts of the RCP and CDP Matrices	32	(3)
On The Consistency of CDP Matrices	35	(8)
Two Evaluative Criteria	43	(1)
A Simulation Evaluation of Different Scales	44	(6)
Analysis of the Computational Results	50	(3)
Conclusions	53	(4)
Deriving Relative Weights from Ratio Comparisons	57	(16)
Background Information	57	(1)
The Eigenvalue Approach	58	(2)
Some Optimization Approaches	60	(1)
Considering The Human Rationality Factor	61	(4)
First Extensive Numerical Example	65	(1)
Second Extensive Numerical Example	66	(1)
Average Error per Comparison for Sets of Different Size	67	(5)
Conclusions	72	(1)
Deriving Relative Weights from Difference Comparisons	73	(14)
Background Information	73	(3)
Pairwise Comparisons of Relative Similarity	76	(9)
Quantifying Pairwise Comparisons of Relative Similarity	76	(1)
Processing Pairwise Comparisons of Relative Similarity	77	(2)
An Extensive Numerical Example	79	(6)
Conclusions	85	(2)
A Decomposition Approach for Evaluating Relative Weights Derived from Comparisons	87	(28)
Background Information	87	(1)
Problem Description	88	(3)
Two Solution Approaches	91	(4)
A Simple Approach	91	(1)
A Linear Programming Approach	92	(3)
An Extensive Numerical Example	95	(2)
Some Computational Experiments	97	(3)
Analysis of the Computational Results	100	(12)
Conclusions	112	(3)
Reduction of Pairwise Comparisons Via a Duality Approach	115	(16)
Background Information	115	(1)
A Duality Approach for Eliciting Comparisons	116	(4)
An Extensive Numerical Example	120	(4)
Applying the Primal Approach	121	(1)
Applying the Dual Approach	122	(2)
Some Numerical Results for Problems of Different Sizes	124	(4)
Conclusions	128	(3)
A Sensitivity Analysis Approach for MCDM Methods	131	(46)
Background Information	131	(2)
Description of the Two Major Sensitivity Analysis Problems	133	(2)
Problem 1: Determining the Most Critical Criterion	135	(20)
Definitions and Terminology	135	(2)
Some Theoretical Results in Determining the Most Critical Criterion	137	(1)
Case (i): Using the WSM or the AHP Method	137	(1)
An Extensive Numerical Example for the WSM Case	138	(4)
Case (ii): Using the WPM Method	142	(1)
An Extensive Numerical Example for the WPM Case	143	(2)
Some Computational Experiments	145	(10)
Problem 2: Determining the Most Critical aij Measure of Performance	155	(10)
Definitions and Terminology	155	(2)
Determining the Threshold Values Ti,j,k	157	(1)
Case (i): When Using the WSM or the AHP Method	157	(1)
An Extensive Numerical Example When the WSM or the AHP Method is Used	158	(3)
Case (ii): When Using the WPM Method	161	(1)
An Extensive Numerical Example When the WPM Method is Used	161	(4)
Conclusions	165	(2)
Appendix to Chapter 8	167	(1)
Calculation of the δ1,1,2 Quantity When the AHP or the WSM Method is Used	167	(2)
Calculation of the δ1,1,2 Quantity When the WPM Method is Used	169	(1)
Calculation of the τ3,4,5 Quantity When the WSM Method is Used	170	(1)
Calculation of the τ3,4,5 Quantity When the AHP Method is Used	171	(3)
Calculation of the τ3,4,5 Quantity When the WPM Method is Used	174	(3)
Evaluation of Methods for Processing a Decision Matrix and Some Cases of Ranking Abnormalities	177	(24)
Background Information	177	(1)
Two Evaluative Criteria	177	(2)
Testing the Methods by Using the First Evaluative Criterion	179	(7)
Testing the Methods by Using the Second Evaluative Criterion	186	(6)
Analysis of the Computational Results	192	(2)
Evaluating the TOPSIS Method	194	(3)
Conclusions	197	(4)
A Computational Evaluation of the Original and the Revised AHP	201	(12)
Background Information	201	(1)
An Extensive Numerical Example	202	(4)
Some Computational Experiments	206	(6)
Conclusions	212	(1)
More Cases of Ranking Abnormalities When Some MCDM Methods Are Used	213	(22)
Background Information	213	(2)
Ranking Irregularities When Alternatives Are Compared Two at a Time	215	(5)
Ranking Irregularities When Alternatives Are Compared Two at a Time and Also as a Group	220	(3)
Some Computational Results	223	(5)
A Multiplicative Version of the AHP	228	(2)
Results from Two Real Life Case Studies	230	(3)
Comparative Ranking Analysis of the ``Bridge Evaluation'' Problem	230	(2)
Comparative Ranking Analysis of the ``Site Selection'' Problem	232	(1)
Conclusions	233	(2)
Fuzzy Sets and Their Operations	235	(6)
Background Information	235	(1)
Fuzzy Operations	236	(2)
Ranking of Fuzzy Numbers	238	(3)
Fuzzy Multi-Criteria Decision Making	241	(22)
Background Information	241	(1)
The Fuzzy WSM Method	242	(2)
The Fuzzy WPM Method	244	(1)
The Fuzzy AHP Method	245	(2)
The Fuzzy Revised AHP Method	247	(1)
The Fuzzy TOPSIS Method	248	(2)
Two Fuzzy Evaluative Criteria for Fuzzy MCDM Methods	250	(7)
Testing the Methods by Using the First Fuzzy Evaluative Criterion	251	(4)
Testing the Methods by Using the Second Fuzzy Evaluative Criterion	255	(2)
Computational Experiments	257	(5)
Description of the Computational Results	258	(3)
Analysis of the Computational Results	261	(1)
Conclusions	262	(1)
Conclusions and Discussion for Future Research	263	(4)
The Study of MCDM Methods: Future Trends	263	(1)
Lessons Learned	263	(4)
References	267	(8)
Subject Index	275	(8)
Author Index	283	(6)
About the Author	289