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2000 | Buch

Introduction to Multi-Criteria Decision Making Kapitel lesen Erstes Kapitel lesen

Multi-criteria Decision Making Methods: A Comparative Study

verfasst von: Evangelos Triantaphyllou

Verlag: Springer US

Buchreihe : Applied Optimization

Enthalten in: Professional Book Archive

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction to Multi-Criteria Decision Making
Abstract
The analysis of the way people make decisions (prescriptive theories) or the way people ought to make decisions (normative theories) is perhaps as old as the recorded history of mankind. Of course, not all these analyses were characterized by the rigorous scientific approaches we see in the literature today. Therefore, it is not surprising that the literature in decision making is humongous and continuously increasing. At the same time, however, the development of the perfect decision making method for rational real life decision making still remains an elusive goal. This contradiction between the extensiveness of the study on this subject and the elusiveness of the final goal of the real life applicability of the findings, constitutes in a way the ultimate decision making paradox.
Evangelos Triantaphyllou
Chapter 2. Multi-Criteria Decision Making Methods
Abstract
With the continuing proliferation of decision methods and their variants, it is important to have an understanding of their comparative value. Each of the methods uses numeric techniques to help decision makers choose among a discrete set of alternative decisions. This is achieved on the basis of the impact of the alternatives on certain criteria and thereby on the overall utility of the decision maker(s). The difficulty that always occurs when trying to compare decision methods and choose the best one is that a paradox is reached, i.e., What decision-making method should be used to choose the best decision-making method? This problem is examined in Chapter 9.
Evangelos Triantaphyllou
Chapter 3. Quantification of Qualitative Data for MCDM Problems
Abstract
The first step in any MCDM problem is to define the set of alternatives and the set of decision criteria that the alternatives need to be evaluated with. Although this is an enormously critical step, its formulation cannot easily be captured with a standard modeling procedure. This task appeals more to the art aspect of MCDM than to the science one. It is this realization that makes most experts in this area to preach that the single most important step in solving any MCDM (and for that reason any decision making) problem is to first correctly define the problem. The interested reader may want to refer to the classic book with the characteristic fables by Russell L. Ackoff [Ackoff, 1978] on the art and science of decision making.
Evangelos Triantaphyllou
Chapter 4. Deriving Relative Weights from Ratio Comparisons
Abstract
As it was mentioned in Chapter 3, an important issue in MCDM methods is to be able to determine the relative weights of importance of a collection of entities (such as the alternatives to be studied in terms of a single decision criterion). This task is similar and closely related to the problem of determining the degree of membership of the elements of a fuzzy set. Usually, such values are between 0 and 1 and they add up to 1. Such weights of degrees of membership are supposed to be a good model of the way people perceive categories [Dubois and Prade, 1980]. Often, the most representative members in the set are assigned to the value of 1 and non-members to the value of 0. Then, the main problem is to determine the degree of membership (i.e., a number between 0 and 1) of the between members. Psychologists [Lakoff, 1973] have found that people can easily identify representative members in a fuzzy set, while they have difficulties in identifying the other members. The importance of evaluating the membership degrees in applications of fuzzy set theory in engineering and scientific fields is best illustrated in the more than 1,800 references given in [Gupta, et al., 1979] (see also Chapter 12 for discussions on some related problems).
Evangelos Triantaphyllou
Chapter 5. Deriving Relative Weights from Difference Comparisons
Abstract
The previous two chapters analyzed the case of eliciting information from the decision maker(s) by means of a number of pairwise comparisons. However, in other related domains such information may be elicited in terms of difference pairwise comparisons. That is, instead of asking questions of the type “How many times is item A more important than item B under criterion X?”, now such questions look like “How much is item A more important than item B under criterion X?”.
Evangelos Triantaphyllou
Chapter 6. A Decomposition Approach for Evaluating Relative Weights Derived from Comparisons
Abstract
As it was described in the previous chapters, pairwise comparisons play an important role in MCDM problems. They often provide an effective and efficient manner for eliciting qualitative information from the decision maker(s). However, a severe drawback of their application is the often large number of them. If there are n objects (also called entities, elements, or concepts) to be analyzed, then a complete set of pairwise comparisons is of size n(n−1)/2. This chapter describes an approach for reducing this number without severely affecting the benefits of having redundancy in the data elicitation process.
Evangelos Triantaphyllou
Chapter 7. Reduction of Pairwise Comparisons Via a Duality Approach
Abstract
As it was discussed in previous chapters, an appealing approach for eliciting qualitative data for an MCDM problem is to use pairwise comparisons. Next suppose that a decision maker wishes to elicit the relative priorities, or weights of importance, of n entities via a sequence of pairwise comparisons. As before, these n entities could be the decision criteria, or the alternatives to be examined in terms of a single decision criterion in some MCDM problem. Then, as it was illustrated in Chapter 3, the decision maker must elicit the value of n(n−1)/2 pairwise comparisons. Therefore, if an MCDM problem involves m alternatives and n decision criteria (multiple hierarchical levels are not considered at this point), then the total number of the required pairwise comparisons is equal to n(n−1)/2 + n(m(m−1)/2).
Evangelos Triantaphyllou
Chapter 8. A Sensitivity Analysis Approach for MCDM Methods
Abstract
There is considerable research on sensitivity analysis for some operations research and management science models such as linear programming, inventory models, and investment analysis (e.g., [Wendel, 1992] and [Triantaphyllou, 1992]). However, research on sensitivity analysis for deterministic MCDM models is rather limited. A brief overview of the related literature can be found in [Triantaphyllou and Sanchez, 1997]).
Evangelos Triantaphyllou
Chapter 9. Evaluation of Methods for Processing a Decision Matrix and Some Cases of Ranking Abnormalities
Abstract
The MCDM methods presented in the second chapter are among the most widely used ones. As it will be seen in the following sections, however, the part of the methods that processes a decision matrix (i.e., step 3 in Section 2.2) may give different answers to the same problem. Because only the WPM, the AHP, the revised AHP, and the TOPSIS method are applicable both in single- and multi- dimensional decision making, these are the methods that are examined in this chapter (i.e., the WSM will not be tested). The ELECTRE method (as described in Chapter 2) was not tested because it is already known that this method presents a different ranking philosophy and it does not assume that a unique ranking always exists in practice. The main part of this chapter is based on the research results presented in [Triantaphyllou and Mann, 1989] plus some additional investigations.
Evangelos Triantaphyllou
Chapter 10. A Computational Evaluation of the Original and the Revised AHP
Abstract
As it was mentioned in Chapter 1, the typical problem examined by the AHP consists of a set of alternatives and a set of decision criteria. Since this problem is very common in many engineering, science, and economic applications, the AHP has been a very popular decision tool. Another reason which contributed to the wide use of the AHP in such applications, is the development of the Expert Choice software (http://​www.​expertchoice.​com). Furthermore, many other computer packages have been developed and are based on the principles of the AHP. A prime example is the Criterium Decision Plus package by Info Harvest, Inc. (http://​www.​ infoharvest.​com). For an excellent description of this package the interested reader may want to read the review in [Haerer, 2000].
Evangelos Triantaphyllou
Chapter 11. More Cases of Ranking Abnormalities when some MCDM Methods are used
Abstract
Chapter 9 presented an evaluation of the AHP, the revised AHP, the WPM, and the TOPSIS methods in terms of two evaluative criteria. Another evaluation was presented in Chapter 10 for the AHP and the revised AHP methods. The issue of evaluating MCDM methods is a controversial one in the decision analysis / decision making communities. This chapter is partially based on some recent developments that are presented in [Triantaphyllou, 2000] and are related to the evaluation of MCDM methods. The present chapter continues on the same subject and presents some new ranking abnormalities when the AHP and some of its variants are used.
Evangelos Triantaphyllou
Chapter 12. Fuzzy Sets and Their Operations
Abstract
For a long time it has been recognized that an exact description of many real life physical situations may be virtually impossible. This is due to the high degree of imprecision involved in real world situations. Zadeh, in his seminal papers [Zadeh, 1965; and 1968], proposed fuzzy set theory as the means for quantifying the inherent fuzziness that is present in ill-posed problems (which by many accounts are the majority of the real life problems in decision making). Fuzziness is a type of imprecision which may be associated with sets in which there is no sharp transition from membership to nonmembership [Bellman and Zadeh, 1970]. Examples of fuzzy sets are classes of objects (entities) characterized by such adjectives as large, small, serious, simple, approximate, etc. [Bellman and Zadeh, 1970].
Evangelos Triantaphyllou
Chapter 13. Fuzzy Multi-Criteria Decision Making
Abstract
In this chapter four deterministic MCDM methods of the ones presented in the second chapter are fuzzified. These are the WSM, the WPM, the AHP (original and ideal mode), and the TOPSIS method. The ELECTRE is not examined (since the TOPSIS method seems to be superior to it). The multiplicative AHP (as described in Section 11.4) is not studied either since it has the same numerical properties as the WPM model. Some crisp MCDM methods have been fuzzified in [Buckley, 1985], [Laarhoven, et al., 1983], and [Lootsma, 1989; and 1997]. The methodology which we are going to explore is different from the methods introduced in the previous three references. In this chapter we will fuzzify the crisp MCDM methods under the assumption that only one decision maker is involved. The developments presented in this chapter are based on the work reported in [Triantaphyllou and Lin, 1996].
Evangelos Triantaphyllou
Chapter 14. Conclusions and Discussion for Future Research
Abstract
It is widely accepted today that people do not always behave the way the well studied normative theories say they ought to behave (see, for instance, [Allais and Hagen, 1979], [Bell, et al., 1988], [Ellsberg, 1961], and Raiffa [1984]. Many decision theories (especially game theories) assume that the decision makers are always perfectly rational. Too often, however, important decisions are based on non-scientific clues (see, for instance, [Kadane and Larkey, 1982a; 1982b; and 1983], [McMillan, 1992], [Neale and Bazerman, 1991], [Raiffa, 1982], and [Sebenius, 1992].
Evangelos Triantaphyllou
Backmatter
Metadaten
Titel
Multi-criteria Decision Making Methods: A Comparative Study
verfasst von
Evangelos Triantaphyllou
Copyright-Jahr
2000
Verlag
Springer US
Electronic ISBN
978-1-4757-3157-6
Print ISBN
978-1-4419-4838-0
DOI
https://doi.org/10.1007/978-1-4757-3157-6