Soft Computing

, Volume 23, Issue 9, pp 3167–3189 | Cite as

Novel soft fuzzy rough rings (ideals) of rings and their application in decision making

  • Kuan Yun ZhuEmail author
Methodologies and Application


In this paper, we investigate the relationship among soft sets, rough sets, fuzzy sets and rings. The notion of soft fuzzy rough rings (ideals) of rings is introduced, which is an extended notion of soft rough fuzzy rings (ideals) of rings. It is pointed out that in this paper, we first apply soft fuzzy rough sets to rings. Moreover, we study roughness in rings with respect to a pseudo-soft fuzzy approximation space. Some new soft fuzzy rough operations over rings are explored. In particular, lower and upper soft fuzzy rough rings (ideals) of rings are investigated. Finally, as an application, we put forth an approach to decision making based on soft fuzzy rough sets and offer an actual example.


Pseudo-fuzzy soft set Soft rough fuzzy set Soft fuzzy rough set Soft fuzzy rough ring (ideal) Decision making 



This research is supported by a grant of National Natural Science Foundation of China (11571010 and 61179038).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Computational Science Hubei Key LaboratoryWuhan UniversityWuhanPeople’s Republic of China

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