Bayesian Fuzzy Neural Networks for Uncertainty-Aware Classification Under Limited Supervision
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Abstract
The reliable deployment of deep learning models in safety-critical domains necessitates not only high predictive accuracy but also rigorous uncertainty quantification, particularly when labeled training data is scarce. Standard deterministic neural networks often yield overconfident predictions on out-of-distribution samples and struggle to generalize under limited supervision. To address these critical vulnerabilities, this paper introduces the Bayesian Fuzzy Neural Network, a novel hybrid architecture that integrates the robust interpretability of fuzzy logic systems with the rigorous probabilistic modeling capabilities of Bayesian neural networks. By embedding variational inference within a fuzzy rule-based framework, the proposed model captures both epistemic and aleatoric uncertainties while maintaining structural transparency. The fuzzy inference mechanism partitions the input space into overlapping linguistic regions, which act as a structural prior that significantly reduces the hypothesis space and mitigates overfitting in low-data regimes. Concurrently, the Bayesian treatment of the network parameters provides a mathematical foundation for uncertainty estimation. Comprehensive experiments conducted across diverse classification tasks, ranging from medical diagnostics to industrial fault detection, demonstrate that the proposed architecture significantly outperforms traditional deterministic and purely Bayesian baselines in terms of classification accuracy, calibration metrics, and out-of-distribution detection under limited supervision constraints. The results establish the viability of fusing probabilistic paradigms with fuzzy set theory to create highly robust, uncertainty-aware, and interpretable machine learning systems.
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