Multicriteria analysis in decision making under information uncertainty

Abstract

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bellman–Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models ( 〈 X , M 〉 models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called 〈 X , R 〉 models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example.