On Approximation of Controls by Fuzzy Systems

Wang and Mendel proved (1991) that fuzzy systems with product inference, cen-troid defuzziication, and everywhere positive membership functions (in particular, Gaus-sians, 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 (_?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 _?operations, any defuzziication 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.