STUDIES ON CENTROID TYPE-REDUCTION ALGORITHMS FOR GENERAL TYPE-2 FUZZY LOGIC SYSTEMS

Generally speaking, Karnik-Mendel algorithm is a standard way to calculate the centroid and perform type-reduction (TR) for interval type-2 fuzzy sets and systems. In this paper, an efficient centroid type-reduction strategy for general type-2 fuzzy sets is introduced based on Karnik-Mendel (KM) algorithm, enhanced Karnik-Mendel (EKM) algorithm, enhanced iterative algorithm+stopping condition (EIASC). The strategy uses the result of alpha-plane representation, performs the centroid type-reduction on each alpha-plane, and expands type-reduction algorithms for general type-2 fuzzy logic systems. Simulations performed and compared by each of three types of algorithms show that they usually need only several resolution of alpha values such that the defuzzified values converge to real values. Compared with the exhaustive computation method, the method can tremendously decrease the computation complexity from exponential into linear. So it provides the potential application value for general type-2 fuzzy logic systems.