Tümleyenli Esnek ikili Parçalı Kesişim ve Birleşim İşlemleri Üzerine Daha Fazla Bilgi

Öz

Molodtsov, belirsizlikle başa çıkmak için 1999'da matematiksel bir araç olarak esnek küme teorisini yarattı. O zamandan bu zamana, çok sayıda esnek küme işlemi tanımlanmış ve kullanılmıştır. Bu çalışma, esnek ikili parçalı işlemlerin, tümleyenli esnek ikili parçalı kesişim ve birleşim işlemleri üzerindeki dağılımlarını ortaya koyarak bu yeni esnek küme işlemlerini kullanarak bazı cebirsel yapıların incelenmesi ve elde edilmesi için araştırmacılara ilham vererek esnek küme teorisi literatürüne katkıda bulunmayı amaçlamaktadır.

Anahtar Kelimeler

• Esnek Kümeler
• Esnek Küme İşlemleri
• Koşullu Tümleyenler

More On Complementary Soft Binary Piecewise Intersection And Union Operations

Öz

In order to deal with uncertainty, Molodtsov propoed soft set theory as a mathematical tool in 1999. Since that time, numerous forms of soft set operations have been defined and employed. By establishing the soft binary piecewise operations' distributions over complementary soft binary piecewise intersection and union operations, this study aims to contribute to the literature on soft set theory by giving inspiration to researchers as regards examining and obtaining some algebraic structures using these new soft set operations.

Anahtar Kelimeler

• soft set
• soft set operations
• conditional complements

Kaynakça

1. Molodtsov D. Soft set theory-first results. Comput Math Appl 1999; 37(1), 19-31.
2. Özlü Ş. Interval Valued q- Rung Orthopair Hesitant Fuzzy Choquet Aggregating Operators in Multi-Criteria Decision Making Problems. Gazi University Journal of Science Part C: Design and Technology 2022a; 10 4). 1006-1025.
3. Özlü Ş. Interval Valued Bipolar Fuzzy Prioritized Weighted Dombi Averaging Operator Based On Multi-Criteria Decision Making Problems. Gazi University Journal of Science Part C: Design and Technology 2022b; 10 (4). 841-857.
4. Özlü Ş and Sezgin A., Soft covered ideals in semigroups. Acta Univ. Sapientiae Math 2021; 12 (2). 317-346.
5. Maji PK, Bismas R & Roy AR. Soft set theory. Comput Math Appl 2003; 45 (1), 555-562.
6. Pei D, Miao D. From Soft Sets to Information Systems. In: Proceedings of Granular Computing. IEEE 2005; 2, 617-621
7. Ali MI, Feng F, Liu X, Min WK. Shabir M. On some new operations in soft set theory. Comput Math Appl 2009; 57(9), 1547-1553.
8. Sezgin A, Atagün AO. On operations of soft sets. Comput Math Appl 2011; 61(5), 1457-1467.

9. Sezgin A, Shahzad A, Mehmood A. New Operation on Soft Sets: Extended Difference of Soft Sets. J. New Theory 2019; (27), 33-42.
10. Stojanovic NS. A new operation on soft sets: extended symmetric difference of soft sets. Military Technical Courier 2021; 69(4), 779-791.
11. Çağman N. Conditional complements of sets and their application to group theory. J New Results Sci 2021; 10 (3), 67-74.
12. Sezgin A, Çağman N, Aybek F. New conditional complements of sets and their application to group theory. in press in Information Management and Computer Science 2023a.
13. Aybek F. New restricted and extended soft set operations. MSc, Amasya University, Turkey, 2023, unpublished thesis.
14. Demirci AM. New type of extended operations of soft set: Complementary extended plus, union and theta operations. MSc, Amasya University, Amasya, Turkey, 2023, unpublished thesis.
15. Sarıalioğlu M. New type of extended operations of soft set: Complementary extended gamma, intersection and star operations. MSc, Amasya University, Amasya, Turkey, 2023, unpublished thesis.
16. Akbulut E. New type of extended operations of soft set: Complementary extended lambda and difference operations. MSc, Amasya University, Amasya, Turkey, 2023, unpublished thesis.
17. Eren ÖF, Çalışıcı H. On some operations of soft sets. The Fourth International Conference on Computational Mathematics and Engineering Sciences; 2019; Antalya, Turkey.
18. Yavuz E. Soft binary piecewise operations and their properties. MSc, Amasya University, Amasya, Turkey, 2023, unpublished thesis.
19. Sezgin A, Sarıalioğlu M. New soft set operation: Complementary soft binary piecewise theta operation. in press in Journal of Kadirli Faculty of Applied Sciences 2023b.
20. Sezgin A, Demirci AM. New soft set operation: Complementary soft binary piecewise star operation. Ikonion Joural of Mathematics, 2023; 5(2), 24-52.
21. Sezgin A, Atagün AO. New soft set operation: Complementary soft binary piecewise plus operation. in press in Matrix Science Mathematic 2023.
22. Sezgin A, Çağman N. New soft set operation: Complementary soft binary piecewise difference operation. in press in Osmaniye Korkut Ata University Journal of the Institute of Science and Technology 2023.
23. Sezgin A, Aybek F. New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic 2023; 7(1), 27-45.
24. Sezgin A, Aybek F, Bilgili Güngör N. New soft set operation: Complementary soft binary piecewise union operation.in press in Black Sea Journal of Engineering and Science 2023b.
25. Sezgin A, Aybek F, Atagün AO. New soft set operation: Complementary soft binary piecewise intersection operation. Acta Informatica Malaysia 2023c; 7(1), 38-53.
26. Sezgin A, Yavuz E. New soft set operation: Complementary soft binary piecewise lamda operation, in press in Sinop University Journal of Science 2023b.