Improving the Speed of Center of Sets Type Reduction in Interval Type-2 Fuzzy Systems by Eliminating the Need for Sorting

In the deployment of interval type-2 fuzzy systems, one of the most important steps is the type reduction. The commonly used center of sets type reducer requires the solution of two nonlinear constrained optimization problems. Frequently used approaches to solve them are the Karnik-Mendel algorithms and their variants. However, these algorithms suffer from the need for sorting, which is known to be computationally very expensive. Using the reformulations proposed in this paper for center of sets type reducer, it is possible to eliminate the need for sorting. This makes interval type-2 fuzzy systems more appropriate for cost-sensitive real-time applications. Extensive simulations are presented to illustrate the faster convergence speed of the proposed method over six other enhanced variants of the Karnik-Mendel algorithm as applied to center of sets type reduction of interval type-2 fuzzy systems.