3WC-GBNRS++: A novel three-way classifier with granular-ball neighborhood rough sets based on uncertainty

Three-way decision with neighborhood rough sets (3WDNRS) is adept at addressing uncertain problems involving continuous data by configuring the neighborhood radius. However, on one hand, the inputs of 3WDNRS are individual neighborhood granules, which reduce the decision efficiency and generality; on other hand, the thresholds of 3WDNRS require prior knowledge to be approximately set in advance, making it difficult to apply in cases where such knowledge is unavailable. To address these issues, we introduce granular-ball computing (GBC) into 3WDNRS from the perspective of uncertainty. Firstly, we propose an enhanced granular-ball generation method based on DBSCAN called DBGBC. Subsequently, we present an improved granular-ball neighborhood rough sets model (GBNRS++) by combining DBGBC with a quality index. Furthermore, we construct a three-way classifier with granular-ball neighborhood rough sets (3WC-GBNRS++) based on the principle of minimum fuzziness loss. This approach provides an objective and efficient way to determine the thresholds. To further enhance classification accuracy, we design an adaptive granular-ball neighborhood within the subsequent classification process of 3WC-GBNRS++. Finally, experimental results demonstrate that, 3WC-GBNRS++ almost outperformed other comparison methods in terms of effectiveness and robustness, including 4 state-of-the-art granular-balls-based classifiers and 5 classical machine learning classifiers on 12 public benchmark datasets. Moreover, we discuss the limitations of our work and the outlook for future research.