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

The fact that four-layer feedforward regular fuzzy neural networks with sig moid function in the first hidden layer are capable of approximately repres enting 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 compa ct set. Secondly, by the conclusions related to standard feedforward networ ks, universal approximations of continuous fuzzy valued functions by regula r fuzzy neural networks are obtained. (C) 2001 Elsevier Science B.V. All ri ghts reserved.