A formal approach to fuzzy modeling

| A formalism for coding fuzzy models of dynam-ical 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 coeecients. The proof of this fact provides a constructive algorithm for generating fuzzy models to approximate an arbitrary map on a compact set arbitrarily closely. 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.