Optimal approximation of nonlinear functions by fuzzy systems

Abstract

This paper presents a novel approach to the optimal approximation of nonlinear functions employing fuzzy systems. The proposed approach, which is based on a genetic algorithm, also illustrates the underlying design principles of different parts of a fuzzy system. This insight is facilitated by our definition of characteristic points. To appreciate this concept, an illustrative example is employed. The essence of this paper is the fact that the conventional selection of membership functions does not lead to the best function approximation. It is also demonstrated that while a fuzzy system with triangular membership functions is, in effect, a linear piecewise approximation of a nonlinear function, a fuzzy system with gaussian member functions can be viewed as a nonlinear piecewise approximation of the same nonlinear function.