Derivative information from fuzzy models

Abstract

Universal approximation is the basis of theoretical research and practical application of fuzzy systems. The ability of fuzzy models to model static information has been successfully proven and tested, while on the other hand their limitations in simultaneously modelling dynamical information are well known. Generally, the fuzzy model is a correct zero-order representation of a process or function. However the derivative of its mathematical expression is not necessarily a derivative fuzzy model of the process or function. A perturbed fuzzy system, as a generalization of the traditional fuzzy system, is proposed. It has the ability to uniformly approximate continuous functions and their derivatives on arbitrarily compact sets to the desired degree. © Springer-Verlag Berlin Heidelberg 2007.