George A. Anastassiou
Fuzzy Symmetrized and Perturbed Neural Network Approximation
Neural Parallel and Scientific Computations 33 (2025) 55-82

https://doi.org/10.46719/NPSC2025.33.04

ABSTRACT.
Here we treat the univariate fuzzy quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation symmetrized and perturbed hyperbolic tangent and generalized logistic functions based fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy modulus of continuity of the involved fuzzy function and the fuzzy derivative of the engaged function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy neural networks are with one hidden layer. The foundation of this work is based on positive linear operators generated deterministic real neural networks approximations.

AMS (MOS) Subject Classification: 26E50, 41A17, 41A25, 41A30, 41A36, 47S40.

Keywords and phrases: Fuzzy Neural Network operators, Fuzzy real Analysis, Symmetrization
and Perturbation in Fuzziness, hyperbolic tangent, generalized logistic, Fuzzy Approximation.