General KH controllers are radial basis function interpolators

This paper connects two thoroughly investigated universal approximator techniques to each other. Recently, it has been shown that the input-output function of the general fuzzy KH interpolation method [1, 2] as well as its modification [3] are stable in the mathematical sense, or in other words, they can be considered as universal approximators with respect to the Lp (p ∈ [1,∞]) norm in the space of continuous functions, defined on a compact domain under certain very general conditions. Our result points out that general KH controllers can be placed into the context of radial basis function (RBF) approximation. However, due to some previously achieved results for KH controllers, some conditions concerning the radial basis functions in the approximation scheme can be relaxed. The advantages of the use of combined neuro-fuzzy applications are also addressed with special emphasis on the benefit of applying fuzzy rule interpolation approaches.