Optimal function approximation using fuzzy rules

Abstract

It has been constructively proven by Kosko (1994) that fuzzy systems are universal approximators. However, the proof does not provide an algorithm to build a fuzzy system that approximates an analytically defined function to an arbitrary precision with a minimum number of fuzzy rules. We describe a method that utilizes the information contained in the analytic definition of a function, such as its first and second derivatives, to build a fuzzy system that approximates it.