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Abstract: We investigate a new category of fuzzy-neural networks such as Hybrid Fuzzy Set-based Polynomial Neural Networks (HFSPNN). These networks consist of a genetically optimized multi-layer with two kinds of heterogeneous neurons such as fuzzy set-based polynomial neurons (FSPNs) and polynomial neurons (PNs). We have developed a comprehensive design methodology that helps determine the optimal structure of networks dynamically. The augmented genetically optimized HFSPNN (referred to as gHFSPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of gHFSPNN leads to the selection of preferred nodes (FSPNs or PNs) available within the HFSPNN. In the sequel, 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 the gHFSPNN is demonstrated through intensive experimentation where we use a number of modeling benchmarks—synthetic and experimental datasets are already being used in fuzzy or neurofuzzy modeling. [Copyright &y& Elsevier]