In real-world scenarios, the values of decision attributes in incomplete decision systems frequently exhibit multiple-level characteristics. Attribute reduction, which aims to identify significant attributes in multi-level incomplete decision systems, has emerged as a crucial research topic in recent years. Currently, most existing works on attribute reduction for such systems are limited to a single granularity level. To address this research gap, we propose two algorithms for multi-level incomplete decision systems: C2F and F2C hierarchical attribute reduction (FHAR, CHAR). We first investigate the relations of reducts from the coarse-granularity level to the fine-granularity level, and then analyze the reverse process. By leveraging these inter-level reduct relations, the proposed algorithms can efficiently derive a new reduct for the target granularity level from the reduct of the current level. This knowledge transfer mechanism significantly enhances algorithmic efficiency. We conduct experiments on ten UCI datasets. The experimental results demonstrate that, compared with six other algorithms, the proposed algorithms achieve significantly higher computational efficiency. Four metrics are employed for classification evaluation, and the results indicate that the proposed algorithms exhibit promising classification performance. The classification accuracy of the algorithms changes slightly with the variation in classifier parameters and data missing rates. Therefore, the proposed algorithms achieve high efficiency, competitive classification performance, and strong robustness.
Gu et al. (Tue,) studied this question.