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.

Granular-ball computing (GBC) proposed by Xia adaptively generates a different neighborhood for each object, resulting in greater generality and flexibility. Moreover, GBC greatly improves the efficiency by replacing point input with granular-ball. However, the current GB-based classifiers rigidly assign a specific class label to each data instance and lacks of the necessary strategies to address uncertain instances. These far-fetched certain classification approachs toward uncertain instances may suffer considerable risks. In this paper, we introduce three-way decision (3WD) into GBC to construct a novel three-way decision with fuzzy granular-ball rough sets (3WD-FGBRS) from the perspective of uncertainty. This helps to construct reasonable multi-granularity spaces for handling complex decision problems with uncertainty. Firstly, 3WD-FGBRS is constructed in a data-driven method based on fuzziness, which avoids the subjective definition of certain risk parameters when calculating the threshold pairs. Based on 3WD-FGBRS, we further propose a sequential three-way decision with fuzzy granular-ball rough sets (S3WD-FGBRS) and analyze the fuzziness loss of multilevel decision result in S3WD-FGBRS. Then, the optimal granular-ball space selection mechanism of S3WD-FGBRS is introduced by combining fuzziness and granular-ball space distance. Finally, extensive comparative experiments are conducted with 3 state-of-the-art GB-based classifiers and 3 classical machine learning classifiers on 12 public benchmark datasets. The results show that our models almost outperform other comparison methods in terms of effectiveness, efficiency and robustness.

Multi-label classification represented by hierarchical classification (HC) plays an important role in current large-scale problems, which can acquire a more accurate expression of data that conforms to the human multi-granularity cognitive process. To compress the original dataset and simultaneously enhance the expressive force of models, selecting an appropriate granularity for approximately describing the classification is the main task in the rough set theory. Nevertheless, the current rough set theory merely concerns flat classification and encounters new problems when approximately describing HC. 1) There lacks a measure to correctly reflect misclassification in accordance with the hierarchical accuracy of HC on the training set. 2) There lacks a measure relying on the distribution of the dataset to reflect the difference between two distinct feature sets describing HC in generalization ability. To address the mentioned issues, this paper utilizes the knowledge distance to characterize HC and proposes a cost-sensitive granularity selection for HC. First, HC and features are respectively granulated according to hierarchical quotient space and neighborhood granular structures. Then, knowledge distance and its extended form are employed to formulate misclassification and test costs. On this basis, a cost-sensitive neighborhood granularity selection is presented for HC. Finally, we experimentally demonstrate the excellent performance of the proposed method in terms of efficiency and HC accuracy both in synthetic and real datasets.