Attribute reduction for hierarchical classification based on improved fuzzy rough set

Attribute reduction plays a critical role in extracting valuable information from high-dimensional datasets. Compared to Pawlak rough set, fuzzy rough set can preserve more data information, making it a prominent focus in the research of attribute reduction. However, current fuzzy rough set-based attribute reduction focuses on flat classification, neglecting distinguishable stability information in hierarchical classification, which leads to insufficient data utilization and reduces the accuracy of attribute reduction. To address these issues, this paper presents two types of fuzzy rough set, named IFRS-I and IFRS-II. Especially, IFRS-I is an improved fuzzy rough set for flat classification, while IFRS-II is constructed based on IFRS-I for hierarchical classification. Unlike traditional fuzzy rough set, IFRS-II has the following two advantages: (1) a stability factor is designed to measure the stability difference among decision classes, (2) a tolerance index is designed to represent the tolerance distance between decision classes based on the approximate information of different decision classes in hierarchical classification. Finally, a stable and effective attribute reduction based on IFRS-II (ARIFRS-II) is designed for hierarchical classification. Experiments demonstrate that compared with the existing related algorithms, ARIFRS-II obtains a higher classification accuracy and stability, while maintaining a suitable number of subsets after reduction.