Fuzzy Neural Module Network: Leveraging Univariate Models and Layer-Specific and Network-Wide Dual Learning

In this study, we propose an incrementally expanding fuzzy neural module network (FNMN) designed to effectively handle both low- and high-dimensional problems without relying on dimensionality reduction techniques. The proposed framework adopts a modular and hierarchical architecture, in which univariate fuzzy neural modules (UFNMs) are incrementally selected and connected according to their representational capability, quantified by the coefficient of determination. The variable-specific univariate fuzzy rule architecture avoids exponential rule growth while preserving interpretability. A residual-driven hierarchy incrementally selects informative modules and progressively refines the model. A hybrid learning strategy combines efficient modulewise learning based on least squares error estimation with global fine-tuning via backpropagation (BP). Adam-based optimization is adopted to enhance convergence stability and reduce sensitivity to learning-rate settings. Extensive experiments on 28 publicly available benchmark datasets demonstrate the effectiveness of the proposed approach. The proposed method achieves an average performance improvement of 19% compared with a conventional fuzzy clustering-based model across diverse benchmarks. Statistical significance tests further confirm that the proposed model significantly outperforms recent neurofuzzy systems. Notably, competitive predictive performance is attained while model complexity is reduced by more than two orders of magnitude relative to deep learning approaches. These findings highlight the efficiency and scalability of the proposed framework.