A New Approach to the Development of Genetically Optimized Multilayer Fuzzy Polynomial Neural Networks

In this paper, the authors propose and investigate a new category of neurofuzzy networks-fuzzy polynomial neural networks (FPNNs)-and develop a comprehensive design methodology involving mechanisms of genetic optimization and, in particular, genetic algorithms (GAs). The conventional FPNNs developed so far are based on mechanisms of self-organization and evolutionary optimization. The design of the network exploits the extended group method of data handling, with some essential parameters of the network being provided by the designer and kept fixed throughout the overall development process. This restriction may hamper a possibility of producing an optimal architecture of the model. The design proposed in this paper addresses this issue. The augmented genetically optimized FPNN (gFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison with the one encountered in the conventional FPNN. The GA-based design procedure that is applied to each layer of FPNN leads to the selection of the preferred nodes (or fuzzy polynomial neurons) available within the FPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs, whereas the ensuing, detailed parametric optimization is carried out in the setting of a standard least-square-method-based learning. The performance of gFPNN is quantified through experimentation where a number of modeling benchmarks are being used, i.e., synthetic and experimental data already experimented within fuzzy or neurofuzzy modeling. The obtained results demonstrate superiority of the proposed networks over the existing fuzzy and neural models