ON APPROXIMATION OF CONTROLS BY FUZZY SYSTEMS

Wang and Medel proved (1991) that fuzzy systems with product inference, centroid defuzzification, and everywhere positive membership functions (in particular, Gaussians, Wang, 1992) are capable of approximating any real continuous control function on a compact set to arbitrary accuracy. Kosko (1992) proved that fuzzy systems, in which membership functions have compact support, and combination operation (V-operation) for rules is the sum, are also universal approximators. In this paper, we generalize this result of Kosko and prove that for any &- and V-operations, any defuzzification procedure, and any basic membership function with a compact support, the resulting fuzzy controls are universal approximators. Also, Wang's result is transfered to min-inference.