‎Fuzzy Ordinary and Fractional General Sigmoid Function Activated‎ ‎Neural Network Approximation

Transactions on Fuzzy Sets and Systems

مقاله 3، دوره 2، شماره 2، بهمن 2023، صفحه 15-38   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2023.1979163.1063

نویسنده

George A Anastassiou^*

Department of Mathematical Sciences, University of Memphis Memphis, TN 38152, U.S.A.

چکیده

Here we research the univariate fuzzy ordinary and fractional quantitative‎ ‎approximation of fuzzy real valued functions on a compact interval by‎ ‎quasi-interpolation general sigmoid activation function relied on fuzzy neural‎ ‎network operators‎. ‎These approximations are derived by establishing fuzzy‎ ‎Jackson type inequalities involving the fuzzy moduli of continuity of the‎ ‎function‎, ‎or of the right and left Caputo fuzzy fractional derivatives of‎ ‎the involved function‎. ‎The approximations are fuzzy pointwise and fuzzy‎ ‎uniform‎. ‎The related feed-forward fuzzy neural networks are with one hidden‎ ‎layer‎. ‎We study in particular the fuzzy integer derivative and just fuzzy‎  ‎continuous cases‎. ‎Our fuzzy fractional approximation result using higher‎ ‎order fuzzy differentiation converges better than in the fuzzy just‎ ‎continuous case‎.

کلیدواژه‌ها

General sigmoid activation function‎؛ ‎Neural‎ ‎network fuzzy fractional approximation‎؛ ‎Fuzzy quasi-interpolation operator‎؛ ‎Fuzzy modulus of continuity‎؛ ‎Fuzzy derivative and fuzzy fractional‎ ‎derivative‎

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