Representing Fuzzy Systems Universal Approximators

Abstract

The described representation of a fuzzy system enables an approximate functional characterization of the inferred output of the fuzzy system. With polynomial subsystem inferences, the approximating function is a sum of polynomial terms of orders depending on the numbers of input membership functions. The constant, linear, and nonlinear parts of the fuzzy inference can hence be identified. The present work also includes two applications which show that the procedure can very well approximate the differential equations. In the case of no analytical solution, the procedure is a good alternative.