Attribute Reduction for Incomplete Hybrid Data Based on Generalized Granular-Ball Neighborhood Rough Set and Overlap Degree Function

Abstract As an effective mathematical framework for modeling fuzziness, inaccuracy, and uncertainty, neighborhood rough sets have been widely applied to attribute reduction and other data mining tasks. Existing neighborhood rough set methods generally rely on fixed neighborhood parameters to construct neighborhoods, which may fail to capture local variations in data distributions. To address this problem, a generalized granular-ball neighborhood rough set model incorporating an overlap degree function is proposed for attribute reduction in incomplete hybrid data. The proposed algorithm adopts a heterogeneous distance function for measuring difference in incomplete hybrid data and generates generalized granular balls using a purity-driven farthest-point bisection strategy, thus reducing repeated recalculations of granular-ball centers and radii. Based on the obtained generalized granular balls, a dual-constrained neighborhood model is developed by integrating generalized granular-ball structural information with neighborhood radius constraints. Candidate attributes are ranked according to the overlap degree, and the developed $$(\alpha ,\lambda )$$ -generalized granular-ball dependency degree function based on relative inclusion degree is used to guide subsequent greedy deletion for obtaining reducts that preserve dependency. Experimental results show that the proposed method achieves the best average rankings in terms of accuracy, macro-F1 score, and macro-recall with both KNN and RF classifiers. Statistical tests further demonstrate that the proposed method achieves statistically significant improvements over some comparison methods on specific evaluation metrics when using the KNN classifier. Ablation experiments further demonstrate that attribute ranking based on the overlap degree improves reduction results on some datasets, whereas generalized granular-ball partitioning captures local classification structures and maintains a reasonable balance between reduction rate and classification performance. These findings support the feasibility and effectiveness of the proposed algorithm.