Consistency of Information About Type-2 Fuzzy Preference Relation

Abstract

In this paper, an axiomatic approach to Pareto set reduction problem is considered. The reduction is based on accounting for preferences of a decision maker which are modeled with the use of a type-2 fuzzy binary relation. This relation is only partially known through a set of so-called information quanta. Since these quanta are provided by the decision maker, it must be verified that they are consistent with the requirements of the axiomatic approach — the axioms of rational choice. Several theorems giving necessary and sufficient conditions of quanta consistency are proved. Ideas for dealing with inconsistencies are discussed with a few examples.