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Applications of repeat degree to coverings of neighborhoods

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Abstract

Covering of neighborhoods is an important concept in covering-based rough sets. There are many unsolved issues related to coverings of neighborhoods. The concept of repeat degree is proposed to study under what condition a covering of neighborhoods is a partition. It enables us to deal with many issues related to coverings of neighborhoods when coverings are incomplete. This paper applies repeat degree to solve some fundamental issues in coverings of neighborhoods. First, we investigate under what condition a covering of neighborhoods is equal to the reduct of the covering which induces the covering of neighborhoods. Then we study under what condition two coverings induce the same relation and the same covering of neighborhoods. Finally, we propose an approach to calculate coverings through repeat degree.

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Acknowledgments

This work is in part supported by the National Natural Science Foundation of China under Grant Nos. 61170128, 61379049, and 61379089, the Natural Science Foundation of Fujian Province, China under Grant No. 2012J01294, the Fujian Province Foundation of Higher Education under Grant No. JK2012028, the Key Project of Education Department of Fujian Province under Grant No. JA13192, and the Zhangzhou Municipal Natural Science Foundation under Grant No. ZZ2013J03.

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  1. Lab of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China

    Hua Yao & William Zhu

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  1. Hua Yao
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  2. William Zhu
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Correspondence to William Zhu.

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Yao, H., Zhu, W. Applications of repeat degree to coverings of neighborhoods. Int. J. Mach. Learn. & Cyber. 7, 931–941 (2016). https://doi.org/10.1007/s13042-014-0287-4

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