A NEW SOFT SET OPERATION: COMPLEMENTARY EXTENDED STAR OPERATION

Abstract

Soft set theory has established itself as a valuable mathematical framework for tackling issues marked by uncertainty, demonstrating its applicability across a range of theoretical and practical fields since its inception. Central of this theory is the operations of soft sets. To enhance the theory and to make a theoretical contribution to the theory, a new type of soft set operation, called “complementary extended star operation” for soft set, is proposed. An exhaustive examination of the properties of this operation has been undertaken, including its distributions over other soft set operations, with the goal of clarifying the relationship between the complementary extended star operation and other soft set operations. This paper also attempts to make a contribution to the literature of soft sets in the sense that studying the algebraic structure of soft sets from the standpoint of soft set operations offers a comprehensive understanding of their application as well as an appreciation of how soft set can be applied to classical and nonclassical logic.

Keywords

• Soft Set
• Soft Set Operations
• Complementary Extended Soft Set Operations

References

1. D. Molodtsov, “Soft set theory-first results”, Computers and Mathematics with Applications, 37 (1), pp. 19-31, 1999.
2. P.K. Maji, R. Bismas, A.R. Roy, “Soft set theory”, Computers and Mathematics with Applications, 45 (1), pp. 555-562, 2003.
3. D. Pei and D. Miao, “From Soft Sets to Information Systems”, In: Proceedings of Granular Computing IEEE, 2, pp. 617-621, 2005.
4. M. I. Ali, F. Feng, X. Liu, W. K. Min., M. Shabir, “On some new operations in soft set theory”, Computers and Mathematics with Applications, 57(9), pp. 1547-1553, 2009.
5. A. Sezgin, A. O. Atagün, “On operations of soft sets”, Computers and Mathematics with Applications, 61(5), pp. 1457-1467, 2011.
6. M.I. Ali, M. Shabir, M. Naz, “Algebraic structures of soft sets associated with new operations”, Computers and Mathematics with Applications, 61, pp. 2647–2654, 2011.
7. A. Sezgin, A. Shahzad, A. Mehmood, “New operation on soft sets: Extended difference of soft sets”, Journal of New Theory, (27), pp. 33-42, 2019.
8. N.S. Stojanovic, “A new operation on soft sets: extended symmetric difference of soft sets”, Military Technical Courier, 69(4), pp.779-791, 2021.

9. Ö. F. Eren, H. Çalışıcı, “On some operations of soft sets”, The Fourth International Conference on Computational Mathematics and Engineering Sciences, Antalya, 2019.
10. A. Sezgin, H. Çalışıcı, “A comprehensive study on soft binary piecewise difference operation”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B -Teorik Bilimler, 12 (1), pp. 32-54, 2024.
11. N. Çağman, “Conditional complements of sets and their application to group theory”, Journal of New Results in Science, 10(3), pp. 67-74, 2021.
12. A. Sezgin, N. Çağman, A.O. Atagün, F.N Aybek, “Complemental binary operations of sets and their application to group theory,” Matrix Science Mathematic, 7(2), pp. 114-121, 2023.
13. F. N. Aybek, New restricted and extended soft set operations, Master of Science Thesis, Amasya University, The Graduate School of Natural and Applied Sciences, Amasya, 214pp, 2024.
14. A.Sezgin, A., A.O. Atagün, “New soft set operation: Complementary soft binary piecewise plus operation”, Matrix Science Mathematic, 7 (2), pp. 125-142, 2023.
15. A. Sezgin, F.N. Aybek, “New soft set operation: Complementary soft binary piecewise gamma operation”, Matrix Science Mathematic, 7 (1), pp. 27-45, 2023.
16. A. Sezgin, F.N. Aybek, A.O. Atagün, “New soft set operation: Complementary soft binary piecewise intersection operation”, Black Sea Journal of Engineering and Science, 6 (4), pp.330-346, 2023.
17. A. Sezgin, F.N. Aybek, N.B Güngör, “New soft set operation: Complementary soft binary piecewise union operation”, Acta Informatica Malaysia, 7 (1), pp.38-53, 2023.
18. A. Sezgin, A.M. Demirci, “New soft set operation: complementary soft binary piecewise star operation”, Ikonion Journal of Mathematics, 5 (2), pp.24-52, 2023.
19. A. Sezgin, E. Yavuz, “New soft set operation: Complementary soft binary piecewise lambda operation”, Sinop University Journal of Natural Sciences, 8 (2), pp. 101-133, 2023.
20. A. Sezgin, N. Çağman, “New soft set operation: Complementary soft binary piecewise difference operation”, Osmaniye Korkut Ata University Journal of the Institute of Science and Technology, 7 (1), pp. 58-94, 2024.
21. A. Sezgin, K. Dagtoros, “Complementary soft binary piecewise symmetric difference operation: A novel soft set operation,” Scientific Journal of Mehmet Akif Ersoy University, 6 (2), pp. 31–45, 2023.
22. A. Sezgin, M. Sarıalioğlu, “New soft set operation: Complementary soft binary piecewise theta operation”, Journal of Kadirli Faculty of Applied Sciences, 4(2), pp. 1-33, 2023.
23. E. Akbulut, New type of extended operations of soft sets: Complementary extended difference and lamda operations, Master of Science Thesis, Amasya University, The Graduate School of Natural and Applied Sciences, Amasya, 89pp, 2024
24. A.M. Demirci, New type of extended operations of soft sets: Complementary extended union, plus and theta operations, Master of Science Thesis, Amasya University, The Graduate School of Natural and Applied Sciences, Amasya, 204pp, 2024.
25. A. S. Sezer, “Certain Characterizations of LA-semigroups by soft sets”, Journal of Intelligent and Fuzzy Systems, 27 (2), pp. 1035-1046, 2014.
26. A.S. Sezer, N. Çağman, A.O. Atagün, “Uni-soft substructures of groups”, Annals of Fuzzy Mathematics and Informatics, 9 (2), pp. 235–246, 2015.
27. A. Sezgin, “A new view on AG-groupoid theory via soft sets for uncertainty modeling”, Filomat, 32(8), pp. 2995–3030, 2018.
28. T. Mahmood, Z.U. Rehman, A. Sezgin, “Lattice ordered soft near rings”, Korean Journal of Mathematics, 26 (3), pp. 503-517, 2018.
29. E. Muştuoğlu, A. Sezgin, Z.K. Türk, “Some characterizations on soft uni-groups and normal soft uni-groups”, International Journal of Computer Applications, 155 (10), pp. 1-8, 2016.
30. A. Sezgin, A.O. Atagün, N. Çağman, H. Demir, “On near-rings with soft union ideals and applications”, New Mathematics and Natural Computation, 18(2), pp. 495-511, 2022.
31. Ş. Özlü, A. Sezgin, “Soft covered ideals in semigroups”, Acta Universitatis Sapientiae Mathematica, 12 (2), pp. 317-346,2020.
32. C.Jana, M. Pal, F. Karaaslan, A. Sezgin, (2019), “(α, β)-soft intersectional rings and ideals with their applications” New Mathematics and Natural Computation, 15 (2), pp. 333–350.
33. A. Sezgin, E. Yavuz, “A new soft set operation: Soft binary piecewise symmetric difference operation”, Necmettin Erbakan University Journal of Science and Engineering, 5 (2), pp. 189-208, 2023.
34. E. Yavuz, Soft binary piecewise operations and their properties, Master of Science Thesis, Amasya University, The Graduate School of Natural and Applied Sciences, Amasya, 244pp, 2024.
35. S. Pant, K. Dagtoros, M.I. Kholil, A. Vivas, “Matrices: Peculiar determinant property”, Optimum Science Journal, 1, pp. 1–7, 2024.