A Hybridization of Modified Rough Bipolar Soft Sets and TOPSIS for MCGDM

Abstract

Uncertain data is a challenge to decision-making (DM) problems. Multi-criteria group decision-making (MCGDM) problems are among these problems that have received much attention. MCGDM is difficult because the existing alternatives frequently conflict with each other. In this article, we suggest a novel hybrid model for an MCGDM approach based on modified rough bipolar soft sets (MRBSs) using a well-known method of technique for order of preference by similarity to ideal solution (TOPSIS), which combines MRBSs theory and TOPSIS for the prioritization of alternatives in an uncertain environment. In this technique, we first introduce an aggregated parameter matrix with the help of modified bipolar soft lower and upper matrices to identify the positive and negative ideal solutions. After that, we define the separation measurements of these two solutions and compute relative closeness to choose the best alternative. Next, an application of the proposed technique in the MCGDM problem is introduced. Afterward, an algorithm for this application is developed, which is illustrated by a case study. The application demonstrates the usefulness and efficiency of the proposal. Compared to some existing studies, we additionally present several merits of our proposed technique. Eventually, the paper handles whether additional studies on these topics are needed.

Keywords

• Bipolar soft sets
• bipolar soft rough sets
• MRBSs
• TOPSIS
• MCGDM

References

1. L. A. Zadeh, Fuzzy Sets, Information and Control 8 (3) (1965) 338–353.
2. D. Molodtsov, Soft Set Theory–First Results, Computers and Mathematics with Applications 37 (4-5) (1999) 19–31.
3. P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Computers and Mathematics with Applications 45 (2003) 555–562.
4. M. I. Ali, F. Feng, X. Liu, W. K. Minc, M. Shabir, On Some New Operations in Soft Set Theory, Computers and Mathematics with Applications 57 (2009) 1547–1553.
5. N. Çağman, S. Enginoğlu, F. Çıtak, Fuzzy Soft Set Theory and Its Applications, Iranian Journal of Fuzzy Systems 8 (3) (2011) 137–147.
6. T. M. Al-Shami, A. Mhemdi, Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications, Journal of Mathematics 8 (2021) 1–2.
7. Z. Pawlak, Rough Sets, International Journal of Computing and Information Science 11 (1982) 341–356.
8. Z. Pawlak, A. Skowron, Rudiments of Rough Sets, Information Sciences 177 (2007) 3–27.

9. F. Feng, C. Li, B. Davvaz, M. I. Ali, Soft Sets Combined with Fuzzy Sets and Rough Sets: A Tentative Approach, Soft Computing 14 (9) (2010) 899–911.
10. F. Feng, X. Liu, V. Leoreanu-Fotea, Y. B. Jun, Soft Sets and Soft Rough Sets, Information Sciences 181 (2011) 1125–1137.
11. M. Shabir, M. I. Ali, T. Shaheen, Another Approach to Soft Rough Sets, Knowledge-Based System 40 (2013) 72–80.
12. T. Shaheen, B. Mian, M. Shabir, F. Feng, A Novel Approach to Decision Analysis Using Dominance-Based Soft Rough Sets, International Journal of Fuzzy Systems 21 (3) (2019) 954–962.
13. M. Shabir, M. Naz, On Bipolar Soft Sets (2013) 18 pages, https://arxiv.org/abs/1303.1344.
14. F. Karaaslan, S. Karataş, A New Approach to Bipolar Soft Sets and Its Applications, Discrete Mathematics, Algorithms and Applications 7 (4) (2015) 1550054 14 pages.
15. T. Mahmood, A Novel Approach Towards Bipolar Soft Sets and Their Applications, Journal of Mathematics 2020 (2020) Article ID 4690808 11 pages.
16. M. Naz, M. Shabir, On Fuzzy Bipolar Soft Sets, Their Algebraic Structures and Applications, Journal of Intelligent and Fuzzy Systems 26 (4) (2014) 555–562.
17. T. M. Al-Shami, Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications, Complexity 2021 (2021) Article ID 6621 854 14 pages.
18. F. Karaaslan, N. Çağman, Bipolar Soft Rough Sets and Their Applications in Decision Making, Afrika Matematika 29 (2018) 823–839.
19. M. Shabir, R. Gul, Modified Rough Bipolar Soft Sets, Journal of Intelligent and Fuzzy Systems 39 (3) (2020) 4259–4283.
20. R. Gul, M. Shabir, M. Naz, M. Aslam, A Novel Approach towards Roughness of Bipolar Soft Sets and Their Applications in MCGDM, IEEE Access 9 (2021) 135102–135120.
21. R. Gul, M. Shabir, Roughness of a Set by (α, β)-Indiscernibility of Bipolar Fuzzy Relation, Computational and Applied Mathematics 39 (3) (2020) 1–22.
22. C. L. Hwang, K. Yoon, Multiple Attribute Decision Making: Methods and Applications, SpringerVerlag, New York, 1981.
23. C. T. Chen, Extensions of the TOPSIS for Group Decision Making under Fuzzy Environment, Fuzzy Sets and Systems 114 (2000) 1–9.
24. Y. Chen, C. Y. Tsao, The Interval-Valued Fuzzy TOPSIS Method and Experimental Analysis, Fuzzy Sets and Systems 159 (11) (2008) 1410–1428.
25. J. P. Brans, P. Vinvke, B. Mareschal, How to Select and How to Rank Projects: The PROMETHEE Method, European Journal of Operation Research 24 (1986) 228–238.
26. J. Ali, Z. Bashir, T. Rashid, On Distance Measure and TOPSIS Model for Probabilistic IntervalValued Hesitant Fuzzy Sets: Application to Healthcare Facilities in Public Hospitals, Grey Systems: Theory and Application 12 (1) (2022) 197–229.
27. S. Eraslan, A Decision Making Method via TOPSIS on Soft Sets, Journal of New Results in Science (8) (2015) 57–71.
28. S. Eraslan, F. Karaaslan, A Group Decision Making Method Based on TOPSIS under Fuzzy Soft Environment, Journal of New Theory (3) (2015) 30–40.
29. M. Shabir, R. Mushtaq, M. Naz, An Algebraic Approach to N-Soft Sets with Application in Decision-Making Using TOPSIS, Journal of Intelligent and Fuzzy Systems 41 (1) (2021) 819– 839.
30. M. Akram, M. Arshad, Bipolar Fuzzy TOPSIS and Bipolar Fuzzy ELECTRE-I Methods to Diagnosis, Computational and Applied Mathematics 39 (1) (2020) 1–21.
31. M. Akram, A. Adeel, TOPSIS Approach for MAGDM Based on Interval-Valued Hesitant Fuzzy N-Soft Environment, International Journal of Fuzzy Systems 21 (3) (2019) 993–1009.
32. Z. Xu and X. Zhang, Hesitant Fuzzy Multi-Attribute Decision-Making Based on TOPSIS with Incomplete Weight Information, Knowledge Based System 52 (2013) 53–64.
33. X. Zhang, Z. S. Xu, Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets, International Journal of Intelligent Systems 29 (2014) 1061–1078.
34. S. H. Mousavi-Nasab, A. Sotoudeh-Anvari, A Comprehensive MCDM-Based Approach Using TOPSIS, COPRAS and DEA as an Auxiliary Tool For Material Selection Problems, Materials and Design 121 (2017) 237–253.
35. T. Mahmood, K. Hussain, J. Ahmmad, U. Rehman, M. Aslam, A Novel Approach Towards TOPSIS Method Based on Lattice Ordered T-Bipolar Soft Sets and Their Applications, IEEE Access 10 (2022) 69727–69740.
36. K. Hayat, M. I. Ali, F. Karaaslan, B. Y. Cao, M. H. Shah, Design Concept Evaluation Using Soft Sets Based on Acceptable and Satisfactory Levels: An Integrated TOPSIS and Shannon Entropy, Soft Computing 24 (2020) 2229–2263.
37. M. A. Alghamdi, N. O. Alshehri, M. Akram, Multi-Criteria Decision-Making Methods in Bipolar Fuzzy Environment, International Journal of Fuzzy Systems 20 (6) (2018) 2057–2064.
38. J. Nan, T. Wang, J. An, Intuitionistic Fuzzy Distance Based TOPSIS Method and Application to MADM, International Journal of Fuzzy System Applications 5 (1) (2016) 43–56.
39. F. Feng, Soft Rough Sets Applied to Multicriteria Group Decision Making, Annals of Fuzzy Mathematics and Informatics 2 (1) (2011) 69–80.
40. M. Saeed, Z. Anam, T. Kanwal, I. Saba, F. Memoona, M. F. Tabassum, Generalization of TOPSIS from Soft Set to Fuzzy Soft Sets in Decision Making Problem, Scientific Inquiry and Review 1 (1) (2017) 11–18.
41. M. Sarwar, Decision-making Approaches Based on Color Spectrum and D-TOPSIS Method under Rough Environment, Computational and Applied Mathematics 39 (4) (2020) 1–32.