‎fuzzy ordinary and fractional general sigmoid function activated‎ ‎neural network approximation

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.