**7. Conclusions**

This paper proposes the MGRS model in terms of IFS based on soft binary relations over two universes. First of all, we defined granulation roughness based on two soft binary relations using IFSs with respect to the aftersets and foresets. In this way, we obtain two

IFSSs with respect to the aftersets and foresets. Some properties of OMGIFRS have been studied. Then, we generalized these concepts to granulation roughness of an IFS based on multi-soft relations and discussed their properties. We presented a decision-making algorithm regarding the aftersets and foresets with an example in practical decision-making problem. In IFS, the sum of membership degree, non-membership degree and hesitant degree of an element is less than or equal to 1. However, in some decision-making problems, the sum of membership degree, non-membership degree and hesitant degree of an element may be greater than 1. In this case, the Pythagorean fuzzy set which is an extension of IFS is the better set to deal with uncertainty. The Pythagorean fuzzy set extension makes better improvement in applicability and flexibility of IFS. Further work may be discussed about investigation of pessimistic MGRS of an IFS based on soft relations. Other OMGIFRS models with interval valued IFSs, uncertain linguistic FSs, basic uncertain information SSs, linguistic Z-number FSSs and Pythagorean FSs may be discussed in future.

**Author Contributions:** Conceptualization, S.B. and M.S.; methodology, M.Z.A.; software, S.B.; validation, M.G.A.; formal analysis, M.Z.A.; investigation, M.Z.A.; resources, M.G.A.; data curation, M.S.; writing—original draft preparation, M.Z.A.; writing—review and editing, S.B.; visualization, M.Z.A.; supervision, S.B.; project administration, M.Z.A.; funding acquisition, M.G.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** We did not use any data for this research work.

**Acknowledgments:** The researchers would like to thank the Deanship of Scientific Research, Qassim University for funding the publication of this project.

**Conflicts of Interest:** The authors declare that they have no conflicts of interest.
