Multivariate Fuzzy Approximation by Neural Network Operators Induced by Several Sigmoid Functions Revisited

Abstract

AbstractHere are researched in terms of multivariate fuzzy complete approximation to the multivariate unit sequences of multivariate fuzzy arctangent-algebraic-Gudermannian-generalized symmetrical activation functions based neural network operators. These operators are multivariate fuzzy analogs of earlier studied multivariate Banach space valued ones. The derived results generalize earlier Banach space valued ones into the fuzzy level. Here the high order multivariate fuzzy pointwise and uniform convergences with rates to the multivariate fuzzy unit operator are given through multivariate fuzzy Jackson type inequalities involving the multivariate fuzzy moduli of continuity of the mth order (\(m\ge 0\)) H -fuzzy partial derivatives, of the involved multivariate fuzzy number valued function. The treated operators are of averaged, quasi-interpolation, Kantorovich and quadrature types at the multivariate fuzzy setting. It follows [29].