New efficient algorithms for the centroid of an interval type-2 fuzzy set

Abstract

In a type-2 fuzzy logic system , one of the important operations is to calculate the centroid of an interval type-2 fuzzy set (IT2 FS). In this paper, two novel algorithms called binary algorithms are proposed to calculate the centroid of IT2 FSs. Then, the outputs of the proposed binary algorithms are proven to be the optimal values. After analyzing the computational complexities of Karnik-Mendel (KM) algorithms, enhanced Karnik-Mendel (EKM) algorithms, enhanced iterative algorithms based on stopping condition (EIASC) algorithms and the proposed binary algorithms, it is found that the proposed binary algorithms are superior to the KM algorithms, EKM algorithms and EIASC algorithms. Finally, two extended binary algorithms are proposed to compute the centroid of an IT2 FS. The efficiencies of the proposed binary algorithms and extended binary algorithms are demonstrated by extensive simulations.