Fuzzy set-oriented neural networks based on fuzzy polynomial inference and dynamic genetic optimization

In this paper, we introduce a new topology and offer a comprehensive design methodology of fuzzy set-based neural networks (FsNNs). The proposed architecture of the FsNNs is based on the fuzzy polynomial neurons formed through a collection of ‘if-then’ fuzzy rules, fuzzy inference, and polynomials with the extended structure of the premise and the consequence parts of fuzzy rules being formed within the networks. Three different forms of regression polynomials (namely constant, linear, and quadratic) are used in the consequence part of the rules. In order to build an optimal FsNN, the underlying structural and parametric optimization is supported by a dynamic search-based genetic algorithm (GA), which forms an optimal solution through successive adjustments (refinements) of the search range. The structure optimization involves the determination of the input variables included in the premise part and the order of the polynomial forming the consequence part of the rules. In the study, we explore two types of optimization methodologies, namely a simultaneous tuning and a separate tuning. GAs are global optimizers; however, when being used in their generic version, they often lead to a significant computing overhead caused by the need to explore an excessively large search space. To eliminate this shortcoming and increase the effectiveness of the optimization itself, we introduce a dynamic search-based GA that results in a rapid convergence while narrowing down the search to a limited region of the search space. We exploit this optimization mechanism to be completed both at the structural as well as the parametric level. To evaluate the performance of the proposed FsNN, we offer a suite of several representative numerical examples.