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On the structure of definable sets in covering approximation spaces

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Abstract

Covering rough sets, a generalization of the classical rough sets, are main research topics of rough set theory. Various covering rough set models have been proposed. In this paper, ten important types of covering rough set models are first reviewed. The algebraic structures of definable sets, inner definable sets and outer definable sets in these covering rough sets are then investigated. Based on the concept of definable sets, we further explore relations among the ten covering rough sets. Finally, the conditions for neighborhood \(\{N(x):x\in U\}\) to form a partition of the universe U are discussed, and an open problem proposed by Yun et al. is answered.

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Acknowledgments

This work was supported by grants from the National Natural Science Foundation of China (Nos. 10971186, 71140004 and 11061004), the Natural Science Foundation of Fujian Province (Nos. JK2011031, 2011J01374), the Department of Education of Fujian Province (No. JA11171) and the Science Foundation of Zhangzhou Normal University in China (No. SJ1015).

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Authors and Affiliations

  1. Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, 363000, People’s Republic of China

    Jinkun Chen & Jinjin Li

  2. Department of Computer Science and Engineering, Zhangzhou Normal University, Zhangzhou, 363000, People’s Republic of China

    Yaojin Lin

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  1. Jinkun Chen
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  2. Jinjin Li
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  3. Yaojin Lin
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Correspondence to Jinkun Chen.

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Chen, J., Li, J. & Lin, Y. On the structure of definable sets in covering approximation spaces. Int. J. Mach. Learn. & Cyber. 4, 195–206 (2013). https://doi.org/10.1007/s13042-012-0086-8

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