This paper presents a hybrid fuzzy wavelet neural network (HFWNN) realized with the aid of polynomial neural networks (PNNs) and fuzzy inference-based wavelet neurons (FIWNs). Two types of FIWNs including fuzzy set inference-based wavelet neurons (FSIWNs) and fuzzy relation inference-based wavelet neurons (FRIWNs) are proposed. In particular, a FIWN without any fuzzy set component (viz., a premise part of fuzzy rule) becomes a wavelet neuron (WN). To alleviate the limitations of the conventional wavelet neural networks or fuzzy wavelet neural networks whose parameters are determined based on a purely random basis, the parameters of wavelet functions standing in FIWNs or WNs are initialized by using the C-Means clustering method. The overall architecture of the HFWNN is similar to the one of the typical PNNs. The main strategies in the design of HFWNN are developed as follows. First, the first layer of the network consists of FIWNs (e.g., FSIWN or FRIWN) that are used to reflect the uncertainty of data, while the second and higher layers consist of WNs, which exhibit a high level of flexibility and realize a linear combination of wavelet functions. Second, the parameters used in the design of the HFWNN are adjusted through genetic optimization. To evaluate the performance of the proposed HFWNN, several publicly available data are considered. Furthermore a thorough comparative analysis is covered.