Sufficient conditions on fuzzy logic controllers as universal approximators

We first establish sufficient conditions for two classes of fuzzy logic controllers (FLCs) in Castro (1995) to approximate real polynomials to any degree of accuracy on a compact domain by using techniques different from those in Ying (1994). Then, we give sufficient conditions for them to be universal approximators. Explicit formulas, which can be used to compute the number of fuzzy rules, are provided simultaneously. Compared with the results in Ying (1994), the conditions here are less conservative since they require fewer fuzzy rules to approximate the same function, and the formulas derived here can be used to determine the number of fuzzy rules directly for multivariable polynomials. Sufficient conditions and explicit formulas to estimate the number of fuzzy rules are also provided when the functions to be approximated are not exactly known