STUDY ON IMPROVED ENHANCED KARNIK-MENDEL ALGORITHMS FOR CENTROID TYPE-REDUCTION OF GENERAL TYPE-2 FUZZY LOGIC SYSTEMS

In recent years, general type-2 fuzzy logic systems (GT2 FLSs) have become a hot topic in current academic research. The block of type-reduction (TR) under the guidance of inference plays the central role for T2 FLSs. In early times, the TR algorithms are developed resort to calculating the centroid of interval type-2 fuzzy sets (IT2 FSs). Generally speaking, the computational intensive enhanced Karnik-Mendel (EKM) algorithms are the standard way to perform the centroid TR of interval type-2 fuzzy logic systems (IT2 FLSs). Based on the a-planes representation theory of general type-2 fuzzy sets (GT2 FSs), this paper introduces the improved EKM (IEKM) algorithms to perform the centroid TR of GT2 FLSs. Two computer simulation examples are used to illustrate and analyze the performances of IEKM algorithms. Compared with the most commonly used EKM algorithms, the IEKM algorithms have faster computation speed without loosing calculation accuracy, which provides the potential value for designing and applying T2 FLSs.