On granular-ball fuzzy rough sets and applications in attribute evaluations

Abstract

Granular-ball computing has emerged as a powerful framework for managing uncertainty, offering a more adaptive and interpretable approach to data analysis. In contrast, traditional fuzzy rough sets, which rely on fuzzy relations between individual data points, often suffer from limited granularity control, sensitivity to noise, and difficulties in handling large-scale or complex datasets. Moreover, the point-wise nature of fuzzy relations restricts the ability to capture group-based structural information inherent in real-world data. To address these limitations, we propose the granular-ball fuzzy rough set model, which integrates fuzzy rough set theory with the granular-ball computing paradigm. This novel model represents data in the form of fuzzy granular-balls, each encompassing a group of similar instances, thereby enhancing granularity management and improving robustness against noise and data sparsity. The lower and upper approximations in this model are redefined using these fuzzy granular-balls rather than individual objects, with the purity of each granular-ball directly influencing the certainty and precision of classification boundaries. This approach facilitates smoother and more stable delineations of positive, negative, and boundary regions in uncertain classification tasks. Additionally, the model introduces monotonous fuzzy granular-ball partitions that evolve with expanding attribute sets, providing a practical mechanism for evaluating attribute significance in feature selection. Overall, the proposed model retains the mathematical rigor of traditional fuzzy rough set theory while offering enhanced flexibility, interpretability, and effectiveness in handling real-world uncertain data.