The Lower Approximation Number in Covering-Based Rough Set
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.
KeywordsCovering Rough set The lower approximation number Granular computing
This work is in part supported by The National Nature Science Foundation of Chi- na under Grant Nos. 61170128, 61379049 and 61379089, the Key Project of Education Department of Fujian Province under Grant No. JA13192, the Project of Education De- partment of Fujian Province under Grant No. JA14194, the Zhangzhou Municipal Nat- ural Science Foundation under Grant No. ZZ2013J03, and the Science and Technology Key Project of Fujian Province, China Grant No. 2012H0043.
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