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.

In large-scale decision systems with high dimensions, constructing an efficient feature selection method via an uncertainty measure, has become a critical problem in fuzzy rough sets (FRS). However, the uncertainty method constructed through FRS for feature selection has the following limitations. 1) The composition of the uncertainty caused by fuzzy distance and similarity is neglected, which can not precisely evaluate the uncertainty. 2) The method of measuring uncertainty is to select all the sample for establishing a fuzzy similarity matrix, which leads to substantial time consumption. 3) The efficiency of selecting import features in a nonbatch manner is relatively low. Driven by this, both granular-ball (GB) computing and three-way approximations (TWA) are integrated to guide an uncertainty measure named multigranularity fuzzy entropy (MGFE), which is based on fuzzy distance and similarity, to improve the efficiency of feature selection. The MGFE is primarily recommended for measuring the uncertainty in multigranularity spaces. Therewith, the GB and TWA computing are integrated to compress the sample space to select representative sample. In addition, the MGFE is employed to assess the significance of the features in the representative sample space. Aided by the TWA, an efficient filter-wrapper feature selection with a three-way accelerator is successfully developed. Finally, related experiments illustrate the advancement of our proposed feature selection.s

Machine understanding and thinking require prior knowledge consisting of explicit and implicit knowledge. The current knowledge base contains various explicit knowledge but not implicit knowledge. As part of implicit knowledge, the typical characteristics of the things referred to by the concept are available by concept cognition for knowledge graphs. Therefore, this paper attempts to realize concept cognition for knowledge graphs from the perspective of mining multigranularity decision rules. Specifically, (1) we propose a novel multigranularity three-way decision model that merges the ideas of multigranularity (i.e., from coarse granularity to fine granularity) and three-way decision (i.e., acceptance, rejection, and deferred decision). (2) Based on the multigranularity three-way decision model, an algorithm for mining multigranularity decision rules is proposed. (3) The monotonicity of positive or negative granule space ensured that the positive (or negative) granule space from coarser granularity does not need to participate in the three-classification process at a finer granularity, which accelerates the process of mining multigranularity decision rules. Moreover, the experimental results show that the multigranularity decision rule is better than the two-way decision rule, frequent decision rule and single granularity decision rule, and the monotonicity of positive or negative granule space can accelerate the process of mining multigranularity decision rules.

Feature selection method with rough sets based on incremental learning has the major advantage of the higher efficiency in a dynamic information system, which has attracted extensive research. However, the incremental approximation feature selection with an accelerator (IAFSA) remains ambiguous for a dynamic information system with fuzzy decisions (ISFD). Driven by this concern, the nonincremental approximation feature selection is first presented by fuzzy knowledge distance (FKD). Second, the incremental theory of FKD is constructed with a batch of objects appended to or removed from the dynamic ISFD. Subsequently, an acceleration mechanism to eliminate redundant information granules is developed to reduce the sample space. Eventually, two categories of IAFSA based on FKD are presented. The experiments reflect the efficiency and effectiveness of the developed IAFSA algorithms.