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.