Fuzzy logic controllers are universal approximators

In this paper, we consider a fundamental theoretical question on why does fuzzy control have such a good performance for a wide variety of practical problems. We try to answer this fundamental question by proving that for each fixed fuzzy logic belonging to a wide class of fuzzy logics, and for each fixed type of membership function belonging to a wide class of membership functions, the fuzzy logic control systems using these two and any method of defuzzification are capable of approximating any real continuous function on a compact set to arbitrary accuracy. On the other hand, this result can be viewed as an existence theorem of an optimal fuzzy logic control system for a wide variety of problems