Fuzzy Ordinary and Fractional General Sigmoid Function Activated Neural Network Approximation
Subject Areas : Transactions on Fuzzy Sets and Systems
George Anastassiou
1
(
Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
)
Keywords: General sigmoid activation function, Neural network fuzzy fractional approximation, Fuzzy quasi-interpolation operator, Fuzzy modulus of continuity, Fuzzy derivative and fuzzy fractional derivative,
Abstract :
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.
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