Fuzzy Wavelet Polynomial Neural Networks: Analysis and Design

In this study, we propose a concept of fuzzy wavelet polynomial neural networks (FWPNNs) based on concepts and constructs of polynomial neural networks and fuzzy wavelet neurons (FWNs). These networks exhibit a rule-based architecture while each rule in the FWN consists of the premise part and consequence part. The premise part is realized by using C-means clustering method, while the consequence part is realized by means of wavelet functions whose parameters are estimated with the aid of the least square method. In some sense, the FWPNN can be regarded as a generalized fuzzy wavelet neural network (FWNN). Unlike Gaussian membership functions that are commonly utilized to implement the premise part of the rules in typical FWNNs, C-means method is employed here to overcome a possible curse of dimensionality. Polynomial neural networks (PNNs) are used to express the nonlinearity of a complex system. Furthermore, the particle swarm optimization is used to optimize the design parameters of the proposed network. Based on the PNNs and FWNNs, the proposed FWPNNs take advantages of these two neural networks: it exhibits the abilities to describe high-order nonlinear relations between input and output variables and it is beneficial to describe models impacted by uncertainty. The proposed FWPNNs are applied for time-series prediction and regression problems (e.g., control of dynamic plants). Several well-known modeling benchmarks including regression and time series are considered to evaluate the performance of the proposed FWPNNs. A comparative analysis shows that the proposed FWPNNs result in better performance when comparing with some previous models reported in the literature.