On Some Developments in Positively Bipolar Soft Groups

Rasti Raheem Mohammedamin; Halgwrd Mohammed Darwesh; Adil Kadir Jabbar

doi:10.5269/bspm.81466

Authors

Rasti Raheem Mohammedamin Department of Mathematics, College of Education, University of Garmian
Halgwrd Mohammed Darwesh Department of Mathematics, Sulaimani University, Iraq https://orcid.org/0000-0003-0112-4884
Adil Kadir Jabbar Department of Mathematics, Sulaimani University, Iraq https://orcid.org/0009-0007-6945-2610

DOI:

https://doi.org/10.5269/bspm.81466

Abstract

In this work, we define the concepts of positively bipolar left and right cosets and examine their fundamental properties and structures. Additionally, we define quotient bipolar soft groups. In addition, we also define positively maximal normal bipolar soft groups and the notions of positively simple bipolar soft groups. Moreover, we establish the definitions of positively solvable bipolar soft groups, and we prove several important results.

References

1. Acar, U., Koyuncu, F., Tanay, B., Soft Sets and Soft Rings, Computers and Mathematics with Applications, 59, 3458–3463, (2010).

2. Ali, M. I., Feng, F., Liu, X., Min, W. K., Shabir, M., On some new operations in soft set theory, Comput. Math. Appl., 57, 1547-1553, (2009).

3. Al-shami, T. M., Bipolar soft sets: Relations between Them and Ordinary Points and Their Applications, Complexity, 2021(Article ID 6621854),1-14, (2021).

4. Aslam, M., Abdulla, S., Ullah, KBipolar fuzzy soft sets and it’s applications in decision making problem, arXiv:1303.6932vl [cs.AI], (2013).

5. Babitha, K. V., Snil, J. J., Soft set relations and functions, Computers and Mathematics with Applications, 60,1840-1849, (2010).

6. Bayramov, S., Aras, C. G., Posul, H, A study on bipolar soft metric spaces Faculty of Sciences and Mathematics, 37(10), 3217-3224, (2023).

7. Cagman, N., Enginoglu, S, Soft set theory and uni-int decision making, European Journal of Operational Research, 207, 848-353, (2010).

8. Demirta¸s, N., Dalkilic, O., Binary Bipolar soft sets, Bol. Soc. Paran. Mat., 2023(41), 1-12, (2021). https://doi.org/10.5269/bspm.51003.

9. Fadel, A., Dzul-Kifli, S. C., Bipolar soft functions, AIMS Mathematics, 6(5), 4428–4446, (2021). https://doi.org/10.3934/math.2021262.

10. Hayat, K., Mahmood, T., Some applications of bipolar soft set: characterizations of two isomorphic hemi-rings via BSI-h-ideals, British Journal of Mathematics and Computer Science, 13(2), 1–21, (2015). https://doi.org/10.9734/BJMCS/2016/22028.

11. Karaaslan, F., Ahmad, I., Ullah, A., Bipolar soft groups, Journal of Intelligent and Fuzzy Systems, 31, 651-662, (2016). https://doi.org/10.3233/IFS-162178.

12. Karaaslan, F., Karatas, S., A new approach to bipolar soft sets and its applications, arXiv:1406.2274vl [math. GM], (2014).

13. Karaaslan, F., Ullah, A., Ahmad, I., Normal Bipolar Soft Subgroups, Fuzzy Information and Engineering, 13(1), 79-98, (2021).

14. Mahmood, T., A Novel Approach towards Bipolar Soft Sets and Their Application, Journal of Mathematics 2020, Article ID 4690808, 1-11, (2020).

15. Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Computers and Mathematics with Applications, 45:555–562, (2003).

16. MohammedAmin, R. R., Darwesh, H. M., Jabbar, A. K., Some Contributions to Positively Bipolar soft groups, New Mathematics and Natural Computation, 202-NMNC-2750032, (2025). http://doi.org/10.1142/S1793005727500323.

17. Mohammed, R. A., Bipolar soft Minimal Structures, European Journal of Pure and Applied Mathematics, 18(2), 1-11, (2025).

18. Molodtsov, D. A., Soft set theory-first results. Computers and Mathematics with Applications, 37,19–31, (1999).

19. Naz, M., Shabir, M., On fuzzy bipolar soft sets their algebraic structures and applications, Journal of Intelligent and Fuzzy Systems, 26(4), 1645–1656, (2014). https://doi.org/10.3233/IFS-130844.

20. Sezgin, A., Atag¨un, A. O., Soft groups and normalistic soft groups, Comput. Math. Appl., 62(2), 685-698, (2011).

21. Sezgin, N., Atag¨un, A. O., On operations of soft sets, Comput. Math. Appl., 61, 1457-1467, (2011).

22. Sezgin, A. , Atag¨un, A. O., Cagman, N., A complete study on and-product of soft sets, Sigma Journal of Engineering and Natural Sciences, 43(1), 1-14, (2025). https://doi.org/10.14744/sigma.2025.00002.

23. Shabir, M., Naz, M., On bipolar soft sets, arXiv:1303.1344vl[math.LO], (2013).

24. Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338–353, (1965).

25. Zhang, W. R., Bipolar fuzzy set and relations: A computational framework for cognitive modeling and multiagent decision analysis, Proceedings of the IEEF conference, 305–309, (1994). https://doi.org/10.1109/IJCF.1994.375115.

26. Zhang, W. R., Bipolar fuzzy sets, IEEE International Conference on Fuzzy Systems Proceedings, 1, 835–840,(1998).