Soft Computing

, Volume 23, Issue 14, pp 5327–5351 | Cite as

Novel classes of fuzzy soft \(\beta \)-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making

  • Li Zhang
  • Jianming ZhanEmail author
  • José Carlos R. Alcantud


In this article, we put forward the concepts of fuzzy soft \(\beta \)-minimal descriptions and fuzzy soft \(\beta \)-maximal descriptions and construct four types of fuzzy soft \(\beta \)-neighborhoods. Secondly, we define five kinds of fuzzy soft \(\beta \)-coverings-based fuzzy rough sets and investigate the relationships among them. Furthermore, we investigate under what conditions two different fuzzy soft \(\beta \)-coverings induce the same lower (upper) approximation operators. Then, we introduce the concepts of intersection and union reducible elements. Finally, we put forward the algorithms with respect to the first and the fifth types of fuzzy soft \(\beta \)-coverings-based fuzzy rough sets, respectively. Through comparison, we find that although these two models are different, the obtained results are the same and the complexity of the algorithm based on the fifth type model is easier than the one based on the first model.


Fuzzy soft \(\beta \)-minimal (maximal) description Fuzzy soft \(\beta \)-neighborhood Fuzzy soft \(\beta \)-covering-based fuzzy rough set Attribute reduction Measure degree Multi-criteria fuzzy group decision making 



The authors are extremely grateful to the editor and the anonymous referee for their valuable comments and helpful suggestions which helped to improve the presentation of this paper. This research is partially supported by NNSFC (11461025; 11561023; 61866011).

Compliance with ethical standards

Conflict of interest

All authors declare that there is no conflict of interest regarding the publication of this manuscript.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Li Zhang
    • 1
  • Jianming Zhan
    • 1
    Email author
  • José Carlos R. Alcantud
    • 2
  1. 1.Department of MathematicsHubei University for NationalitiesEnshiChina
  2. 2.BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME)University of SalamancaSalamancaSpain

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