Computing Centroid of General Type-2 Fuzzy Set Using Constrained Switching Algorithm

Abstract

Centroid of general type-2 fuzzy set can be used as a measure of uncertainty in highly uncertain environments. Computing centroid of general type-2 fuzzy set has received an increasing research attention during recent years. Although computation complexity of such sets is higher than that of interval type-2 fuzzy sets, with the advent of new representation techniques, e.g. alpha-planes and z-Slices, computation efforts needed to deal with general type-2 fuzzy sets have decremented. A very first method to calculate the centroid of a general type-2 fuzzy set was to use Karnik-Mendel algorithm on each alpha-plane, independently. Because of the iterative nature of this method, running time in this approach is rather high. To tackle such a 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 alpha-plane, independently, while reducing convergence time compared with other algorithms like iterative use of Karnik-Mendel algorithm on each alpha-plane. The proposed approach is based on estimating an initial switch point for each alpha-plane. Exhaustive computations demonstrate that the proposed method is considerably faster than independent implementation of existing iterative methods on each alpha-plane. (C) 2015 Sharif University of Technology. All rights reserved.