Fuzzy polynomial neural networks: Hybrid architectures of fuzzy modeling

In this paper, we introduce a concept of fuzzy polynomial neural networks (FPNNs), a hybrid modeling architecture combining polynomial neural networks (PNNs) and fuzzy neural networks (FNNs). These networks are highly nonlinear rule-based models. The development of the FPNNs dwells on the technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The structure of the FPNN results from a synergistic usage of FNN and PNN. FNNs contribute to the formation of the premise part of the rule-based structure of the FPNN. The consequence part of the FPNN is designed using PNNs. The structure of the PNN is not fixed in advance as it usually takes place in the case of conventional neural networks, but becomes organized dynamically (through a growth process) to meet the required approximation error. We exploit a group method of data handling (GMDH) to produce this dynamic topology of the network. At the premise part of the FPNN, FNN uses a fuzzy inference method with the learning realized through a standard back propagation. The parameters of the membership functions, learning rates, and momentum coefficients are adjusted with the use of genetic optimization. We also distinguish between two types of the FNN structures showing how this taxonomy depends on the type of a fuzzy partition of input variables. The performance of the FPNN is quantified through experimentation that exploits standard data already used in fuzzy modeling. The obtained experimental results reveal that the proposed networks exhibit high accuracy and generalization capabilities in comparison to other similar fuzzy models.