Fuzzy analytic hierarchy process with interval type-2 fuzzy sets

Abstract

The membership functions of type-1 fuzzy sets have no uncertainty associated with it. While excessive arithmetic operations are needed with type-2 fuzzy sets with respect to type-1's, type-2 fuzzy sets generalize type-1 fuzzy sets and systems so that more uncertainty for defining membership functions can be handled. A type-2 fuzzy set lets us incorporate the uncertainty of membership functions into the fuzzy set theory. Some fuzzy multicriteria methods have recently been extended by using type-2 fuzzy sets. Analytic Hierarchy Process (AHP) is a widely used multicriteria method that can take into account various and conflicting criteria at the same time. Our objective is to develop an interval type-2 fuzzy AHP method together with a new ranking method for type-2 fuzzy sets. We apply the proposed method to a supplier selection problem.