Universal approximations of continuous fuzzy-valued functions by multi-layer regular fuzzy neural networks

Abstract

The fact that four-layer feedforward regular fuzzy neural networks with sigmoid function in the first hidden layer are capable of approximately representing continuous fuzzy valued functions on any compact set of R is shown. At first, Bernstein polynomials associated with fuzzy valued functions are employed to approximate continuous fuzzy valued function defined on a compact set. Secondly, by the conclusions related to standard feedforward networks, universal approximations of continuous fuzzy valued functions by regular fuzzy neural networks are obtained.