Decision Making Based on Possibility Theory

Abstract

In decision-making problems under risk, one of the main tasks is to evaluate the probabilities of the occurrence of such random events that affect the outcomes of alternative decisions. In some specific situations, due to the lack of initial information, it is difficult or even impossible to perform such evaluation. In this article we present an alternative approach to choosing decisions under uncertainty. This approach is based on the possibility theory, which is at the intersection of various developed theories of uncertainty: the theory of fuzzy sets, the theory of evidence and the theory of probabilities. Evaluating the possibilities of relevant events is a simpler task than evaluating the probabilities of these events. The article presents the conceptual foundations of the possibility theory. The use of this theory for decision making is demonstrated with a simple illustrative example.