A New Ranking Approach for General Interval Type 2 Fuzzy Sets Using Extended Alpha Cuts Representation

Abstract

A new ranking methodology for general interval type 2 fuzzy sets (IT2FS) using extended alpha cuts representation is proposed. First, the extended alpha cut representation of the IT2FS is defined. Then, the parametric representation of the type 1 fuzzy sets (T1FS) is formulated by constructing the embedded pessimistic, modal and optimistic functionals. The corresponding parametric centroid functional of the IT2FS is determined. Finally, the average centroid of the IT2FS is calculated by taking the integral average of the parametric centroid functional. In this manner, the IT2FSs are defuzzified and can be ranked by sorting the average centroids. A numerical example is presented for verifying the proposed method.