**6. Conclusions**

The interval-valued soft set is a useful tool to deal with fuzziness and uncertainties in decision-making problems. In this paper, we constructed two crisp topological spaces over the set of objects, and then presented two different preorder relations in these topological spaces. By using a new method for ranking data, we proposed an approach for solving multi-attribute group decision-making problems by using a new method for ranking data. Finally, a real-life example has been presented to verify the proposed method approach and to demonstrate the effectiveness by comparing the results with those of some of the existing approaches.

For future research, it would be of merit to apply the decision-making methods into practical applications such as evaluation systems, recommender systems, and conflict handling.

**Author Contributions:** Formal analysis, A.Z.K.; methodology, A.K. and A.Z.K.; supervision, A.K. and A.Z.K.; validation, A.K.; visualization, A.K.; writing—original draft, M.A.; writing—review & editing, A.K. All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

**Funding:** The second and third authors gratefully acknowledge the Fundamental Research Grant Schemes, Reference No: FRGS/1/2018/STG06/UPM/01/3, awarded by the Ministry of Higher Education Malaysia.

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

**Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank the referees and editors for the useful comments and valuable remarks, which improved the current manuscript substantially.

**Conflicts of Interest:** The authors declare that they have no competing interests.
