GBFRVFL: Granular-Ball Computing-Based Fuzzy Random Vector Functional Link Network

In practical machine learning tasks, data are often contaminated with noise, outliers, and class imbalance, which can degrade the performance of conventional models. While random vector functional link (RVFL) networks offer fast training and strong generalization, they do not explicitly handle uncertainty or exploit local data structure. To address these limitations, we propose a fuzzy granular-ball random vector functional link (GBFRVFL) framework that leverages granular-ball computing to abstract raw samples into adaptive granular balls. Within this framework, we introduce two membership assignment schemes: (i) F-GBRVFL, which incorporates fuzzy membership to quantify the reliability of each granular ball, and (ii) SDAP-GBRVFL, which we propose, incorporates a novel statistical density-adaptive pythagorean membership (SDAPM) scheme that dynamically adjusts membership and non-membership values based on class variance, local sparsity, and granular-ball compactness. These schemes enhance robustness to noise, outliers, class imbalance, and uncertainty in granular-ball distributions, while retaining the computational efficiency of RVFL networks. Extensive experiments on 37 benchmark UCI and KEEL datasets under both clean and noisy conditions demonstrate that the proposed models consistently outperform baseline models, achieving superior accuracy and stability. The results validate the effectiveness of integrating granular-ball computing with adaptive membership schemes for reliable, scalable, and noise-tolerant learning.