Abstract
Covering-based rough set has attracted much research interest with significant achievements. However, there are few analysis that have been conducted to quantify covering-based rough set. The approximation number is viewed as a quantitative tool for analyzing the covering-based rough set. In this paper, we focus on the lower approximation number. Firstly, we investigate some key properties of the lower approximation number. Secondly, we establish a lattice and two semilattice structures in covering-based rough set with the lower approximation number. Finally, based on the lower approximation number, a pair of matroid approximation operators is constructed. Moreover, we investigate the relationship between the pair of matroid approximation operators and a pair of lattice approximation operators.
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Liu, H., & Zhu, W. (2015). The lower approximation number in covering-based rough set. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9436, pp. 222–230). Springer Verlag. https://doi.org/10.1007/978-3-319-25754-9_20
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