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

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. (c) 2021 Elsevier Inc. All rights reserved. For any type-2 fuzzy logic system, it contains a set of type-2 fuzzy rules in which variables are expressed by type-2 fuzzy sets (T2 FSs). When desired inputs are provided, a crisp-valued output deduced from the system will be output after two successive operations type reduction and defuzzification are carried out. Translating a T2 FS into a type-1 fuzzy set (T1 FS) is the main task of type reduction, and the process of defuzzification is to convert that T1 FS into a number. Tan et al. [35] claimed that type reduction apparently cannot be avoided and is much more time consumed than defuzzification. The concept of the centroid of an interval type-2 fuzzy set (IT2 FS) was initiated by Karnik and Mendel [10], which pro