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 typereduction 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.