Enhanced Karnik-Mendel Algorithms for Interval Type-2 Fuzzy Sets and Systems

The Karnik-Mendel (KM) algorithms are iterative procedures widely used in fuzzy logic theory. They are known to converge monotonically and super-exponentially fast; however, several (usually two to six) iterations are still needed before convergence occurs. Methods to reduce their computational cost are proposed in this paper. Extensive simulations show that on average the enhanced KM algorithms can save about two iterations, which corresponds to more than a 39% reduction in computation time.