Analyses of regular fuzzy neural networks for approximation capabilities

Abstract

By introducing a trapezoidal fuzzy function and using the properties of the function, we set up a continuously increasing fuzzy function that cannot be arbitrarily closely approximated on a compact set of F 0(R) by the regular fuzzy neural network (RFNN). Thus, the conclusions in Buckley and Hayashi (Fuzzy Sets and Systems 61 (1994) 43–51) are improved and the problem if the RFNN is the universal approximator to the class of continuously increasing fuzzy functions is solved. Finally, we obtain the universal approximation to the extended fuzzy functions by RFNN.