Integrating multivariate fuzzy neural networks into fuzzy inference system for enhanced decision making

Abstract

In this paper, we introduce a novel family of operators for single-hidden layer feed-forward neural networks that operate on multivariate fuzzy-valued functions. These operators are based on the fractional mean value of the approximating function. The construction of these operators involves the use of sigmoidal functions, providing multiple choices for their implementation. We demonstrate the modeling capabilities of our operators employing a novel combined neural network system that incorporates the basic fuzzy inference mechanism and fuzzy neural networks. This system represents the connection strength among the output neurons using multivariate fuzzy-valued functions, enhancing decision-making processes. Additionally, we prove the convergence properties of these operators with respect to the Pompeiu-Hausdorff metric. By controlling the asymptotic decay of the sigmoidal function, we achieve accurate Jackson-type estimations using the modulus of continuity of fuzzy-valued functions.