‎Fuzzy Ordinary and Fractional General Sigmoid Function Activated‎ ‎Neural Network Approximation

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.

Keywords

• general sigmoid activation function‎
• ‎neural‎ ‎network fuzzy fractional approximation‎
• ‎fuzzy quasi-interpolation operator‎
• ‎fuzzy modulus of continuity‎
• ‎fuzzy derivative and fuzzy fractional‎ ‎derivative‎