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This study presents an innovative approach to the design of a hybrid fuzzy classifier, with a focus on exploring the classification capability of a conventional fuzzy polynomial neural network (CFPNN). The proposed novel self-organizing hybrid fuzzy polynomial NN classifier (HFPNNC) improves performance while maintaining model interpretability and fixability by synergistically combining an adaptive network structure and the compound regularization technique (CRT). Recent studies have focused on exploring the potential of CFPNN structures for addressing regression issues. To effectively introduce the CFPNN framework to multiclassification tasks, a resilient fuzzy polynomial neural network structure was designed as a basic subclassifier to construct the proposed HFPNNC. The proposed HFPNNC employs a dynamically adaptive structure comprising of two types of critical layers: 1) the fuzzy set-based polynomial neurons layers and 2) the polynomial neurons layers. This allows the classifier to adapt to the complexity of classification tasks. To further strengthen the robustness and generalization ability of the HFPNNC, we incorporate the synergistic combination of probabilistic constrained competitive response selection (PCCRS) and ℓ2-norm regularization least squares estimation (ℓ2-LSE) methods to manage the generation of network layers and the estimation of neuron weights. As key constituents of the CRT approach, the PCCRS and ℓ2-LSE method strike a balance between model complexity and performance. The effectiveness of the proposed HFPNNC is thoroughly evaluated against classical classifiers, state-of-the-art fuzzy classifiers and deep learning baseline models using 17 public datasets, two real-world datasets, and three large-scale datasets. HFPNNC achieves the best prediction in 72.7% of the data. The experimental results and the statistical analysis show a remarkable advantage of the HFPNNC over existing methods, confirming its potential as a flexible, interpretable solution for classification tasks.