Multicriteria analysis based on constructing payoff matrices and applying methods of decision making in fuzzy environment

Abstract

There exist two classes of problems, which need the use of a multicriteria approach: problems whose solution consequences cannot be estimated with a single criterion and problems that, initially, may require a single criterion or several criteria, but their unique solutions are unachievable, due to decision uncertainty regions, which can be contracted using additional criteria. According to this, two classes of models ( X, M and X, R models) can be constructed. Analysis of X, M and X, R models (based on applying the Bellman-Zadeh approach to decision making in a fuzzy environment and using fuzzy preference modeling techniques, respectively) serves as parts of a general scheme for multicriteria decision making under information uncertainty. This scheme is also associated with a generalization of the classic approach to considering the uncertainty of information (based on analyzing payoff matrices constructed for different combinations of solution alternatives and states of nature) in monocriteria decision making to multicriteria problems. The paper results are of a universal character and are illustrated by an example.

On multicriteria decision making under conditions of uncertainty

“…It allows one to increase the adequacy of built models and, as consequence, the credibility and factual efficiency of decisions based on their analysis. Taking this into account, it should be noted that the results of [15,16] may serve as a methodological tool for implementing the second way in the consideration of uncertainty in multicriteria decision making.…”

“…The results of [15,16] are associated with the generalization of the classic approach [3,28,35] to deal with the information uncertainty, based on building and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature or scenarios, in monocriteria decision making to multicriteria problems.…”

“…The results of [15,16] are based on combining two branches of mathematics of uncertainty: elements of game theory and fuzzy set theory and do not fit the general approaches to deal with external uncertainties in the multicriteria analysis, classified and analyzed in [8,38] and discussed in more recent works [10,20]. These results, combined with the analysis of hX; Mi models and hX; Ri models (related to individual or group decision making based on fuzzy preference modeling [18,21,22,24,32,33], for instance; considering that hX; Ri models are used for analyzing multiattribute problems, other approaches [26,27,42], for example, may be applied as well) served for developing a general scheme of multicriteria decision making under conditions of uncertainty.…”

“…Examples of applying the generalization of the classic approach dealing with the uncertainty of information to multicriteria decision making are given in [15,16,33]. However, our experience in its use has revealed some limitations, which can lead to contradictory decisions, discussed below.…”

“…The overcoming of these limitations is based on the proposed approach which permits the simultaneous consideration of choice criteria of the classic approach [3,28,35] as objective functions within the framework of hX; Mi models, whose analysis provides the harmonious solutions. Such consideration of choice criteria of the classic approach [3,28,35] is of a fundamental character and serves as the basis for modifying and improving the results of [15,16]. This is convincingly demonstrated by applications examples.…”