Abstract
Occasionally, critical remarks have been made in the literature on each of the proposed basic concepts for MCDM methods. In the following, some critical points central to the methodological discussion in MCDM will be recapitulated. Usually, the most widely spread concepts found the greatest attention in these discussions. On the other hand, rather unknown approaches or the single representatives of a ‘school’ of MCDM methods often met with no response until now. There is also quite few explicit criticism on simple concepts of multicriteria decision aid. Partly, this may be attributed to the ad-hoc appearance of some approaches such that they are supposed to be out of question. Keeney (1988, p. 408), for instance, writes: “Oversimplistic value tradeoffs, such as lexicographic orderings, are often too simplistic”. On the other hand, Stewart (1992) regards the simple additive aggregation as a wide-spread, intuitive, and easy-to-understand method which, in case of doubt, may be preferable to more complex methods just because of this.
“My present design, then, is not to teach the method which each ought to follow for the right conduct of his reason, but solely to describe the way in which I have endeavored to conduct my own. They who set themselves to give precepts must of course regard themselves as possessed of greater skill than those to whom they prescribe; and if they err in the slightest particular, they subject themselves to censure.”
—René Descartes, Discourse on Method.
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References
See also Park (1978)
See Belton and Gear (1983), Islei and Lockett (1988), Dyer (1990a, 1990b), Stewart (1992), Murphy (1993), Carlsson and Walden (1995).
See Harker and Vargas (1990), Saaty (1990, 1994).
See Dyer (1990a, p. 251). Also call for the following Section 2.1.2. where the claim for descriptivity of MCDM methods is put into question. However, Saaty (1997) himself considers such an orientation of the AHP to be central.
See Hannan (1985), Romero (1991).
See Rosenthal (1983).
See also Romero (1986).
See Vetschera (1991).
See, e.g., Hemming (1979). See also the discussion in the following Section 2.1.2.
See Vincke and Tsoukiàs (1992), especially p. 34–37.
See Alley (1983), and also Gershon and Duckstein (1983b).
Considering measurement theory (Roberts (1979), Pfanzagl (1973)) which deals with measurements in the sense of transformations from a considered system (a part from reality) into a formal (mathematical) model, a statement on specific values to be measured is called meaningless if its truth value changes under different feasible scale transformations. For instance, comparisons of additively connected ordinal values (e.g. a weighted sum of criteria) are meaningless. Jaeger (1989) and others point to the relevance of these considerations especially for the area of MCDM. Especially in MCDM analyses or methods, ordinal attributes are often applied or interpreted such that meaningless results are produced. As a result, “the insiders are amused or angry, depending on their temperament and actual mood, while outsiders are often very impressed.” See Jaeger (1989, p. 1).
For instance, during the eleventh (1994) and twelfth (1995) International Conferences on MCDM, discussion circles on this subject have been initiated by Korhonen and Wallenius.
Especially, the first two of these approaches are well-known, e.g. in economics. See also Schneider (1987, p. 15, 36, 54) who distinguishes explaining (or positive) and modeling (or normative) and also metering theories.
See Bell, Raiffa and Tversky (1988, p. 16).
See also Bitz (1981, p. 5f, 75f).
See also Schneider (1987, p. 196, 46f). For instance, the neoclassically oriented modeling and, hence, a main part of economic theory is based on the concept of the separability of mutual dependencies by the assumption of the existence of equilibrium market prices which are determined as the result of a (normative) calculus of optimization. See Schneider (1987, p. 252, 312).
See Bell, Raiffa and Tversky (1988, p. 17).
See Bell, Raiffa and Tversky (1988, p. 11).
See Raiffa (1994).
See Edwards (1992, p. xi).
See Zeleny (1982, p. 416).
See Davey, Olson and Wallenius (1994); also cf. Larichev (1985), Payne (1982) and Sage (1981).
See Popper (1965, p. 121–126).
See Popper (1965, p. 78–92). According to this, the falsification of a theory is done if a basic statement (or statement of observation) is found which contradicts a universal statement (theory statement).
See Moulin (1988).
Also cf. Larichev (1984).
See Tsoukiàs and Vincke (1992).
This is, for instance, discussed in Zeleny (1982). See also Raiffa (1994).
A general treatise of method pluralism in OR is given by Mingers (1996) and Mingers and Brocklesby (1996, 1997) who denote such a fundament also as ‘multimethodology’ and substantiate it with reference to Habermas. Keen (1977) discusses similar aspects in connection with concepts of optimality or optimization and considers multicriteria modeling as a suitable framework to integrate controversial viewpoints.
Roy (1992) considers as a function of MCDM approaches to come to ‘better’ decisions although he regards the possibility of scientifically founding the meaning of ‘better’ as a “virtual impossibility” (p. 17).
See also Silver (1991, p. 31f).
This is, e.g., assumed by Cohon and Marks (1975).
See Hong and Vogel (1991), Jelassi and Ozernoy (1989) and Ozernoy (1988, 1992). In Ozernoy’s work the various difficulties of such a project become evident: It is necessary for developing a corresponding decision support system (DSS) based on AI techniques to identify and to acquire MCDM knowledge. Such knowledge is, however, distributed among the vast MCDM literature and the researchers and practitioners working in that area. Additionally, this knowledge is not free of contradictions. Ozernoy (1988, p. 246) proposes: “… an MCDM expert system probably cannot mimic a human expert. Instead, it must integrate significant knowledge that will be gradually extracted from several MCDM experts and the MCDM literature by knowledge engineers.” But this approach does not point out a solution concerning the given conflicting opinions on the ‘correct’ method.
See, e.g., (1971), Park (1978), Currim and Sarin (1984).
See Daniels (1992).
Hobbs (1986) interprets sensitivity depending on the results of choosing a method or determining its parameters. In order to determine whether the results of different methods or of different settings of the parameters of a method significantly differ from each other, Hobbs proposes an experimental, heuristic proceeding, possibly supported by statistical testing methods. Gershon and Duckstein (1983a) propose as a criterion the robustness with respect to modifications of parameter values of a method which should be judged without referring to a specific MCDM problem to be solved.
See, e.g., Hopcroft and Ullman (1988), Wegener (1989).
For typical computation times for degenerate LP problems see Kruse (1986), especially p. 36.
See Stewart (1992).
An ambitious utilization of graphical representations within a multicriteria decision support system (MCDSS) is, for instance, presented by Korhonen, Wallenius and Zionts (1992).
See, e.g., Lotfi, Yoon and Zionts (1997).
See Buchanan and Daellenbach (1987, p. 355).
See Stewart (1992).
See, e.g., Carlson and Walden (1995).
Also cf. Currim and Sarin (1984) and the discussion in Section 1.2. of this chapter.
See Zeleny (1982, p. 1–11).
For instance, in Hirsch (1976) and Hobbs (1985, 1986).
Seldom in the literature, meta decision problems are formulated explicitly as MCDM method design problems. The only example known to the author is given by Ramesh, Zionts, and Karwan (1986) who analyze two interactive branch and bound methods for integer MOLP problems and deduce two parameterized families of hybrid methods. By doing so, it is possible to combine these two ones and to express the meta decision problem as a problem of choosing a parameter from a continuous set. Two objectives for evaluating the considered methods are proposed: The minimization of the number of questions for the decision maker and the minimization of the solution time. Using these criteria several efficient solutions of the meta decision problems are obtained.
See Mareschal (1988).
In PROMETHEE, the weights do not serve an aggregation of the single objective functions but an additive aggregation of criterion-specific preference functions which result from a pairwise comparison of alternatives, pairwise comparisons Also cf. Section 4. of this chapter. The diversity of methods and their usage of parameters with respect to the obtained results has been analyzed in Hanne (1989).
This model appearing to be simple may be of considerable complexity concerning its solution. Let us note in this connection that on the one hand the parameter ξ depending on the method may require complex data structures, e.g. vectors or matrices. On the other hand, method functions f M are usually nonlinear and nondifferentiable such that optimization methods for ‘hard to be solved’ problems must be employed. In Section 2.2. of Chapter 3 the utilization of evolutionary algorithms is proposed for this purpose because these show good properties with respect to robustness and speed (see Schwefel, 1977) and their global convergence under appropriate conditions (see Bäck, Hoffmeister and Schwefel, 1991, and Rudolph, 1994b) can be proved.
See Arrows (1963) and the discussion in Zeleny (1982).
See, e.g., Hwang and Masud (1979, p. 8).
These are, for instance, the works by Buchanan and Daellenbach (1987), Daellenbach and Buchanan (1989) Goicoechea, Stakhiv and Li (1992), and Wallenius (1975). Besides this, there are analyses based on computer experiments in which a decision maker’s behavior is simulated, e.g. by assuming a given utility function. See, e.g., Khairullah and Zionts (1979, 1987), Mote, Olson, Venkataramanan (1988). By means of these computer experiments only objective information is determined.
See Buchanan and Daellenbach (1987, p. 357).
See, e.g., Rockart and DeLong (1988, p. 17). Some authors (e.g. Donovan and Madnick (1977)) allow also one-time decisions and differentiate institutional and ad-hoc-DSS instead. For Simon (1966) programmed decisions which widely correspond to repetitive ones are central areas of application for computers and thus provide perspectives for automation.
See Saaty (1997, p. 328).
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Hanne, T. (2001). Critical Discourse on the MCDM Methodology and the Meta Decision Problem in MCDM. In: Intelligent Strategies for Meta Multiple Criteria Decision Making. International Series in Operations Research & Management Science, vol 33. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1595-1_2
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