Approximation by Max-Min Neural Network Operators

In this paper, we introduce a max-min approach for approximation by neural network operators activated by sigmoidal functions. Our focus lies in addressing both pointwise and uniform convergence in the context of univariate functions. Then, we investigate the order of approximation. We also take into account the max-min quasi-interpolation operators. Finally, we present several practical applications of our approximation methods, including a comparative analysis between max-min neural network operators and their max-product and linear counterparts, as well as denoising 1D noisy signals.