Fuzzy-driven broad learning system with class probability and density awareness for multi-view data

The broad learning system (BLS) has recently emerged as a promising alternative to deep neural networks, offering comparable predictive accuracy with drastically reduced computational cost through random weight assignment and pseudo-inverse-based training. Despite its efficiency, conventional BLS suffers from a critical limitation: it treats all training samples equally, making it highly sensitive to outliers, label noise, and class imbalance, ubiquitous challenges in real-world data. To overcome these shortcomings, we propose a new framework, the class probability-based bell-shaped BLS (CPBS-BLS). In CPBS-BLS, each sample is assigned an adaptive membership value through a bell-shaped weighting function conditioned jointly on class probability and imbalance ratio. This mechanism automatically emphasizes reliable samples in dense regions while suppressing the influence of outliers and noisy points in sparse regions, leading to a more robust decision boundary. Although CPBS-BLS substantially improves robustness in single-view settings, its reliance on a single perspective restricts its ability to capture complementary structures present in complex, multi-faceted data. To address this, we further advance the framework by introducing the class probability-based bell-shaped multi-view BLS (CPBS-MvBLS). CPBS-MvBLS integrates multiple views of data while preserving the adaptive weighting scheme, enabling the model to exploit complementary information across diverse feature spaces. This joint treatment of sample reliability, class imbalance, and multi-view consistency represents a novel step forward in the BLS paradigm. We provide rigorous theoretical analysis establishing generalization bounds for both CPBS-BLS and CPBS-MvBLS, guaranteeing their reliability. Extensive experiments on benchmark datasets from UCI, KEEL, and AwA demonstrate that our models consistently outperform state-of-the-art baselines in accuracy, robustness to noise, and handling of imbalanced classes, as validated through statistical significance testing. The source code of the proposed CPBS-BLS and CPBS-MvBLS models are available at https://github.com/mtanveer1/CPBS-BLS.