Some extensions of the karnik-mendel algorithms for computing an interval type-2 fuzzy set centroid

Computing the centroid of an interval type-2 fuzzy set is an important operation in a type-2 fuzzy logic system, and is usually implemented by Karnik-Mendel (KM) iterative algorithms. This paper proves that the centroid computation of an interval type-2 fuzzy set (IT2 FS) using KM algorithms is equivalent to the Newton-Raphson root-finding method in numerical analysis, and explains how continuous enhanced KM (CEKM) algorithms can be used to compute that centroid. Weighted enhanced KM (WEKM) algorithms are proposed to connect EKM algorithms and CEKM algorithms together using numerical integration techniques. Three new kinds of centroid computation methods are summarized as root finding, CEKM algorithms and WEKM algorithms. Numerical examples illustrate the applications of these new centroid computation methods, and demonstrate the superity of the WEKM algorithms.