A formal approach to fuzzy modeling

A formalism for coding fuzzy models of dynamical systems is presented. It is shown that the set of models consistent with this formalism contains models that are capable of duplicating the trajectories of an arbitrary conventional discrete time dynamical system, whose one step maps are polynomials with rational coefficients. The formalism also illustrates similarities between fuzzy systems and hybrid control systems that we hope to be able to exploit by extending results from the area of hybrid systems to the fuzzy domain and vice versa