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 R n. 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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This work was supported by National Natural Science Foundation (69974041, 69974006).
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Puyin, L. Approximation capabilities of multilayer feedforward regular fuzzy neural networks. Appl. Math.- J. Chin. Univ. 16, 45–57 (2001). https://doi.org/10.1007/s11766-001-0036-9
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DOI: https://doi.org/10.1007/s11766-001-0036-9