On Multicriteria Choice Based on Type-2 Fuzzy Preference Relation: an Axiomatic Approach

Abstract

A multicriteria choice problem is considered. The setting of this problem includes three objects, namely, a set of feasible alternatives, a numerical vector criterion, and a decision maker's binary strict preference relation. The Edgeworth — Pareto principle is a fundamental instrument to solve multi-criteria problems. Previously, the validity of this principle was established in the case of a crisp as well as a type-1 fuzzy preference relation. We assume that the preference relation is a type-2 fuzzy relation. Under two reasonable axioms the Edgeworth—Pareto principle is established. In accordance with the first axiom, an alternative not chosen in a pair should not be selected from the whole set of feasible alternatives. The second axiom is the Pareto axiom, which provides greater preference for those alternatives that have larger (smaller) values of one or more criteria.