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Operation properties and algebraic properties of multi-covering rough sets

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Abstract

The multi-covering rough sets (MCRSs) are a popular aspect of rough sets. It is easy to see that classical rough sets, covering rough sets (CRSs) and multi-granulation rough sets (MGRSs) are all the special cases of the MCRSs. Recently, the algebraic theory of these rough set models mentioned above have been researched in detail. However, the algebraic theory of MCRSs has not been studied until now. It is necessary for researchers to explore the algebraic theory of MCRSs. In this paper, we focus on the operation and algebraic theories of two types of MCRS models. First, the properties of the two types of multi-covering set approximations are discussed. Especially, the properties of multi-covering approximation operators based on the unary coverings are deeply researched. Second, the operation properties with respect to intersection and union of MCRSs are researched. Meanwhile, to compute the intersection and union of MCRSs, several algorithms are constructed. Finally, on the basis of the operation properties of MCRSs, many meaningful algebraic properties of MCRSs are deeply studied.

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Acknowledgements

The authors are very grateful to the reviewers and editor for their valuable suggestions. This work is partially supported by the National Natural Science Foundation of China (Nos. 61105041, 61472463, 61402064, 61772002), the National Natural Science Foundation of CQ CSTC (No. cstc2015jcyjA40053), the Natural Science Foundation of Fujian Province (Nos.  2017J01763, 2016J01735, 2016J01022, 2016J01310), the Science and Technology Research Program of Chongqing Municipal Education Commission (No. KJ1709221), the Macau Science and Technology Development Foundation (No. 081/2015/A3), the Foundation of Education Department of Fujian Province, China (No. JAT160369), and the Research Startup Foundation of Jimei University (NO. ZQ2017004).

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Authors and Affiliations

  1. School of Science, Jimei University, Xiamen, 361021, Fujian, People’s Republic of China

    Qingzhao Kong

  2. School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, Fujian, People’s Republic of China

    Xiawei Zhang

  3. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, Chongqing, People’s Republic of China

    Weihua Xu

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  1. Qingzhao Kong
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  2. Xiawei Zhang
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  3. Weihua Xu
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Correspondence to Weihua Xu.

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Kong, Q., Zhang, X. & Xu, W. Operation properties and algebraic properties of multi-covering rough sets. Granul. Comput. 4, 377–390 (2019). https://doi.org/10.1007/s41066-018-0137-y

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