Decision-making With a Fuzzy Preference Relation in a Fuzzy Set of Alternatives

A general decision-making problem is considered in which a set of alternatives and a non-strict preference relation specified in this set are of fuzzy nature. The corresponding fuzzy equivalence and strict preference relations are defined which allow to introduce a fuzzy set of non-dominated solutions. It is shown that under some weak topological conditions unfuzzy non-dominated solutions to the problem exist. The questions of equivalence of these solutions are studied and a method of calculating these solutions is suggested.