OPTIMIZATION OF FUZZY MEMBERSHIP FUNCTION USING EXTENDED KALMAN FILTER

Abstract

The performance of fuzzy system depends on both its rule base and its membership function. Given a rule base, the membership function can be optimized in order to obtain the best possible performance from the fuzzy system. Many methods have been used to optimize the fuzzy membership function. We can put them into derivative-free methods and derivative-based methods .Derivative-free methods that have been used include genetic algorithms, neural networks, evolutionary programming, cell mapping, fuzzy equivalence relations and heuristic methods. Derivative-based methods that have been used include Gradient descent, simplex method, least squares and other numerical techniques. Both• methods have some advantages and disadvantages. Derivative-free methods have the advantage that they do not require the derivative of the objective function with respect to the membership function parameters. However, they typically tend to converge more slowly than derivative-based methods .Derivative-based methods have the advantage of fast convergence .However, due to their dependence on analytical derivatives; they are limited to specific objective functions, specific types of inference, and specific types of membership functions. Results show that how the extended Kalman filter can be used to optimize the fuzzy membership function. We see that the Extended Kalman Filter can be an effective tool for improving the performance of a fuzzy system.