An interpretable uncertainty-aware intelligent framework based on generalized multi-scale formal contexts and Bayesian deep neural networks

Modeling uncertainty and interpretability remains challenging in intelligent systems, particularly where complex decision boundaries and ambiguous feature-label relationships coexist. Although Bayesian deep neural networks (BDNNs) offer principled uncertainty quantification, they are constrained by limited prior knowledge, feature redundancy, and opacity. We propose the generalized multi-scale formal context BDNN (Λ-BDNN), an interpretable and uncertainty-aware framework. Λ-BDNN integrates formal concept analysis with Bayesian deep learning. It constructs multi-scale contexts containing conditional and decision attributes to explicitly represent information granularity while preserving semantic structures. Mutual information quantifies attribute interdependencies to enable effective feature selection and reduce redundancy. Furthermore, non-redundant decision rules are derived to filter samples and improve data quality. To enhance robustness, Bayesian optimization is employed to establish a surrogate probabilistic model for automatic hyperparameter configuration. The optimized BDNN subsequently performs intelligent classification under uncertainty-aware constraints. Experimental results on two benchmark datasets demonstrate that the proposed framework consistently outperforms ten representative methods. Additionally, SHapley Additive exPlanations (SHAP) are used for feature analysis; the strong consistency between SHAP and mutual information-based selection further validates the framework's interpretability, effectiveness, and applicability.