Study on reasonable initialization enhanced Karnik-Mendel algorithms for centroid type-reduction of interval type-2 fuzzy logic systems

Type-reduction (TR) is a key block for interval type-2 fuzzy logic systems (IT2 FLSs). In general, Karnik-Mendel (KM) (or enhanced Karnik-Mendel (EKM)) algorithms are used to perform the TR. These two types of algorithms have the advantage of preserving the uncertainties of membership functions (MFs) flow in IT2 FLSs. This paper gives the initialization explanations of KM and EKM algorithms, and proposes reasonable initialization enhanced Karnik-Mendel (RIEKM) algorithms for centroid TR of IT2 FLSs. By considering the accurate continuous Nie-Tan (CNT) algorithms as the benchmark, four computer simulation examples are adopted to illustrate and analyze the performances of RIEKM algorithms for solving the centroid TR and defuzzification of IT2 FLSs. Compared with the EKM algorithms, the proposed RIEKM algorithms have smaller absolute errors and faster convergence speeds, which afford the potential value for designing and applying IT2 FLSs.