Computing Centroid of General Type-2 Fuzzy Sets using Constrained Switching Algorithm

Abstract

Centroid of a general type-2 fuzzy sets can be used as a measure of uncertainty in highly uncertain environments. Computing centroid of general type-2 fuzzy sets has received an increasing research attention during recent years. Although computation complexity of such sets is higher than interval type-2 fuzzy sets but with the advent of new representation techniques, e.g., α-planes and z-slices, computation efforts needed to deal with general type-2 fuzzy sets has decremented. A very first method to calculate the centroid of a general type-2 fuzzy set was to use Karnik-Mendel algorithm on each α-plane, independently. Because of iterative nature of this method, running time in this approach is rather high. To tackle such drawback, several emerging algorithms such as Sampling method, Centroid-Flow algorithm and, recently, Monotone Centroid-Flow algorithm have been proposed. The aim of this paper is to present a new method to calculate centroid intervals of each α-plane independently while reducing convergence time compared with other algorithms like iterative use of Karnik-Mendel algorithm on each α-plane. The proposed approach is based on estimating an initial switch point for each α-plane. Exhaustive computations demonstrate that the proposed method is considerably faster than independent implementation of existing iterative methods on each α-plane.