Abstract
Four-layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on ℱ0 (R)n by the four-layer fuzzy neural networks are shown. At first, multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of Rn. Secondly, by introducing cut-preserving fuzzy mapping, the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.
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