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Covering based multigranulation fuzzy rough sets and corresponding applications

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Abstract

By combining covering based rough sets, fuzzy rough sets, and multigranulation rough sets, we introduce covering based multigranulation fuzzy rough set models by means of fuzzy \(\beta \)-neighborhoods. We investigate axiomatic characterizations of covering based optimistic, pessimistic and variable precision multigranulation fuzzy rough set models. We propose coverings based \(\alpha \)-optimistic (pessimistic) multigranulation fuzzy rough sets and D-optimistic (pessimistic) multigranulation fuzzy rough sets from fuzzy measures. We examine the relationships among these kinds of coverings based fuzzy rough sets. Finally, we apply the proposed models to solve problems for multi-criteria group decision-making.

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Acknowledgements

The authors are extremely grateful to the editor and four anonymous referees for their valuable comments and helpful suggestions which helped to improve the presentation of this paper. This research was partially supported by NNSFC (11461025; 11561023) and a Discovery Grant from NSERC Canada.

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Authors and Affiliations

  1. Department of Mathematics, Hubei Minzu University, Enshi, 445000, China

    Jianming Zhan

  2. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an, China

    Xiaohong Zhang

  3. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2, Canada

    Yiyu Yao

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  1. Jianming Zhan
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  2. Xiaohong Zhang
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Correspondence to Jianming Zhan.

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Zhan, J., Zhang, X. & Yao, Y. Covering based multigranulation fuzzy rough sets and corresponding applications. Artif Intell Rev 53, 1093–1126 (2020). https://doi.org/10.1007/s10462-019-09690-y

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