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Topological approach to multigranulation rough sets

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Abstract

For further studying the theory of multigranulation rough sets, we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to characterize the uncertainty of a multigranulation topological rough space. Finally, based on the invariance of interior and closure operators of a target concept, a granulation selection algorithm is introduced to deal with the granularity selection issue in the multigranulation rough data analysis.

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Acknowledgments

The authors would like to thank the anonymous reviewers and the editor for their constructive and valuable comments. This work is supported by grants from National Natural Science Foundation of China under Grant (No. 71031006), National Key Basic Research and Development Program of China (973) (No. 2013CB329404), Innovative Talents of Higher Learning Institutions of Shanxi, China (No. 20120301), and Education Committee of Fujian Province under Grant (Nos. JK2011031).

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Authors and Affiliations

  1. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, People’s Republic of China

    Guoping Lin, Jiye Liang & Yuhua Qian

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

    Guoping Lin

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  1. Guoping Lin
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  2. Jiye Liang
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  3. Yuhua Qian
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Correspondence to Jiye Liang.

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Lin, G., Liang, J. & Qian, Y. Topological approach to multigranulation rough sets. Int. J. Mach. Learn. & Cyber. 5, 233–243 (2014). https://doi.org/10.1007/s13042-013-0160-x

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