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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Fuzzy Fractional Neural Network Approximation by Fuzzy Quasi-interpolation Operators

Journal of Applied Nonlinear Dynamics 2(3) (2013) 235--259 | DOI:10.5890/JAND.2013.08.002

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

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Abstract

Here we consider the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation sigmoidal and hyperbolic tangent fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the right and left Caputo fuzzy frac-tional derivatives of the engaged function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed- forward fuzzy neural networks are with one hidden layer. Our fuzzy frac- tional approximation results into higher order converges better than the fuzzy ordinary ones.

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