A formal approach to fuzzy modeling

A formalism for coding fuzzy models of dynamical systems is presented. It is shown that the formalism is rich enough to capture the performance of arbitrary conventional discrete time dynamical systems whose transition maps are polynomials with rational coefficients. The proof of this fact provides a constructive algorithm for generating fuzzy models to arbitrarily closely approximate an arbitrary map on a compact set. Our modeling formalism highlights the similarities between fuzzy systems and hybrid control systems, We hope to be able to exploit these similarities by extending results from the area of hybrid systems to the fuzzy domain and vice versa.