This paper presents a strong data-mining method based on a rough set, which can simultaneously realize feature selection, classification, and knowledge representation. Although a rough set, a popular method for feature selection, has good interpretability, it is not sufficiently efficient and accurate to deal with large-scale datasets with high dimensions, which prevents it from being immediately applied to real-world scenarios. To address the efficiency issue of a rough set, we discover the stability of the local redundancy (SLR) of attributes and propose a theorem to prove it rigorously. Based on SLR, only the parts of objects in the boundary region are partitioned when calculating outer significance, which further improves the efficiency of the rough set. With regard to the accuracy issue, we show that overfitting may lead to ineffectiveness of the rough set, especially when processing noise attributes. We then propose relative importance, a robust measurement for an attribute, to alleviate such overfitting issues. In this paper, we propose a novel rough-set framework that significantly improves the efficiency and accuracy of existing rough-set methods. We further develop our rough set framework by proposing a “rough concept tree” for knowledge representation and classification. Experimental results on public benchmark datasets show that our proposed framework achieves higher accuracy than seven state-of-the-art feature-selection methods. All the codes are available athttps://github.com/syxiaa/powerroughset.

Granular computing, a new paradigm for solving large-scale and complex problems, has made significant progresses in knowledge discovery. Granular ball computing (GBC) is a novel granular computing method, which can rapidly generate scalable and robust information granules, that is, granular balls. However, a comprehensive index for measuring the performance of a granular ball does not exist. Furthermore, GBC lacks a mechanism to deal with dynamic decision systems. Therefore, in this study, the quality index of a granular ball is first formulated. Next, with this index, a novel granular ball rough sets model (GBRS) based on GBC is proposed. GBRS is more conducive to learning knowledge from uncertain datasets and more suited to incremental learning than the latest granular ball neighborhood rough sets model based on GBC. Subsequently, an incremental mechanism is introduced into GBRS, and two incremental learning models are developed for objects increasing in stream patterns and batch patterns, respectively. In the incremental learning process, three patterns of granular balls, that is, update, fusion, and split, were well studied when a set of objects was added to the decision system. Finally, to verify the effectiveness and efficiency, we apply GBRS and these two incremental learning models into classification tasks. Compared with four current state-of-the-art classification methods based on granular computing and four classical classifiers in machine learning, the proposed classifiers in this paper achieve higher classification accuracy as well as better efficiency on benchmark datasets.