Abstract:Here we investigate further the univariate fuzzy ordinary and fractional quantitative approximation of fuzzy real valued functions on a compact interval. This is done by quasi-interpolation sigmoid multicomposite activation functions based infinitely many specific and amplified multicomposite fuzzy neural network operators. These approximations are derived by establishing fuzzy multicomposite 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 multicomposite neural networks are with one hidden layer. We study in particular the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional multicomposite approximation result using higher order fuzzy differentiation converges better than in the multicomposite fuzzy just continuous case. All these approximations are generated by 7 specific and basic activation functions.