General fuzzy systems are function approximators

Proves, in a constructive way, that general fuzzy systems can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Furthermore, the author reveals the underlying mechanism of such function approximation: the fuzzy systems can uniformly approximate any polynomials which, according to the Weierstrass approximation theorem, can uniformly approximate any continuous function on a compact domain. It is shown that as the approximation accuracy approaches zero, the number of fuzzy rules needed for the approximation approaches ∞