Studies on Centroid Type-Reduction Algorithms for Interval Type-2 Fuzzy Logic Systems

Type-reduction is one of the most important blocks in interval type-2 (IT2) fuzzy logic systems (FLSs). This paper investigates three types of centroid type-reduction algorithms for interval type-2 fuzzy logic systems. One is the traditional type-reduction algorithm, called Karnik Mendel (KM) algorithm, and the other two are enhanced type-reduction algorithms, called enhanced Karnik Mendel (EKM) algorithm and Enhanced Iterative Algorithm with stopping condition (EIASC). According to two types of primary membership function of interval type-2 fuzzy sets, as the number of sampling points of primary variable increases, simulation results show that the defuzzified values for three types of type-reduction algorithms all converge to certain values. The computational costs of these algorithms are also analyzed. Above these provide a reference to interval type-2 fuzzy logic systems designers and adopters.