Constructive sufficient conditions for fuzzy logic controllers to approximate C1 functions

For a class of fuzzy logic controllers, constructive sufficient conditions under which they can approximate any C¹ functions to any required accuracy on a compact domain are established. Explicit formulas which can be used to calculate the number of fuzzy rules needed are derived simultaneously. For the case that the C¹ functions are polynomials, we also prove that our results are less conservative than the ones in Hao Ying (1994)