General interval type-2 Mamdani fuzzy systems are universal approximators

Abstract

Fuzzy systems using type-2 fuzzy sets and fuzzy logic are important and are indeed gaining increasing attention in the literature (e.g., type-2 fuzzy controllers and fuzzy models). A fundamental question is whether a type-2 fuzzy system is a universal approximator in that it is capable of uniformly approximating any real continuous function on a compact domain to any degree of accuracy. Up to date, no work addressing this issue can be found in the literature. In this paper, we constructively prove that a general class of Mamdani interval type-2 fuzzy systems is universal approximator. This result lays a theoretical foundation for the fuzzy systems development.