Ultimate Possibilities of Pareto Set Reduction Based on Quanta of Fuzzy Information

Abstract

The multicriteria choice problem with a fuzzy preference relation is considered. This problem involves a set of feasible alternatives, a numerical vector criterion, and a fuzzy preference relation of a decision- maker (DM). The concepts of fuzzy vector space, a polyhedral fuzzy set, and the distance between convex fuzzy sets and cones are used. To reduce the Pareto set, ultimate possibilities of using information about the fuzzy preference relation in the form of its quanta are studied. For a sufficiently wide class of choice problems, it is proved that an originally unknown fuzzy set of nondominated elements can be arbitrarily accurately approximated using a finite set of fuzzy information quanta.