Covering based multigranulation fuzzy rough sets and corresponding applications

  • Jianming ZhanEmail author
  • Xiaohong Zhang
  • Yiyu Yao


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.


Multigranulation rough set Covering based fuzzy rough set Fuzzy \(\beta \)-neighborhood Decision making 



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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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsHubei Minzu UniversityEnshiChina
  2. 2.School of Arts and SciencesShaanxi University of Science and TechnologyXi’anChina
  3. 3.Department of Computer ScienceUniversity of ReginaReginaCanada

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