Optimization of rational-powered membership functions using extended Kalman filter

This paper presents an extension to the application of the extended Kalman filter (EKF) in membership function (MF) optimization. Since the EKF is a derivative-based method, and derivative calculations of various MF shapes are too complicated, so far only triangular type has been optimized via this approach. In this article, the EKF is applied in optimizing the rational-powered MFs which are extended form of triangular/trapezoidal functions, and hence can offer better performance in almost all applications. In addition, because of the efficiency of the singleton MFs, which makes them a common and desirable choice in hardware/software realization of fuzzy systems, these MFs are also optimized using the EKF. The corresponding analytical equations and derivative formulas are given, and finally the efficiency of the EKF in MF optimization is discussed.