Yeni Bir Esnek Küme İşlemi: Tümleyenli Esnek İkili Parçalı Lambda (λ) İşlemi

Yıl 2023, Cilt: 8 Sayı: 2, 101 - 133, 28.12.2023

Aslıhan Sezgin Eda Yavuz

https://doi.org/10.33484/sinopfbd.1320420

Öz

Molodtsov, 1999 yılında Esnek Küme Teoriyi belirsizlikle başa çıkmak için bir matematiksel araç olarak ortaya koymuştur. Teori, hem teorik hem de uygulama yönüyle birçok alana uygulanmıştır. 1999 yılından bu yana, farklı çeşitlerde esnek küme işlemleri tanımlanmış ve çeşitli türlerde kullanılmıştır. Bu çalışmada, “tümleyenli esnek ikili parçalı lambda işlemi” adı verilen yeni bir esnek küme işlemi tanımlanmış ve temel cebirsel özellikleri araştırılmıştır. Ayrıca tümleyenli esnek ikili parçalı lambda işleminin genişletilmiş esnek küme işlemleri, tümleyenli genişletilmiş esnek küme işlemleri, esnek ikili parçalı işlemler, tümleyenli esnek ikili parçalı işlemler ve kısıtlanmış esnek küme işlemleri üzerine dağılması incelenerek bu yeni esnek küme işlemi ile diğer esnek küme işlemleri arasındaki ilişkiler elde edilerek esnek kümelerin cebirsel yapılarını ve bazı yeni karar verme yöntemlerini elde etmek için okuyuculara ilham vermek adına esnek küme literatürüne katkı sağlanması amaçlanmaktadır.

Anahtar Kelimeler

Esnek kümeler, esnek küme işlemleri, koşullu tümleyenler

Destekleyen Kurum

YOK

Proje Numarası

YOK

Teşekkür

Makale, ikinci yazar olan Yüksek Lisans öğrencisi Eda YAVUZ'un yüksek lisans tezinin bir bölümünden kesit içermektedir.

A New Soft Set Operation: Complementary Soft Binary Piecewise Lamda (λ) Operation

Öz

In 1999, Molodtsov introduced Soft Set Theory as a mathematical tool to deal with uncertainty. It has been applied to many fields both as theoretical and application aspects. Since 1999, different kinds of soft set operations have been defined and used in various types. In this paper, we define a new kind of soft set operation called, “complementary soft binary piecewise lambda operation” and we handle its basic algebraic properties. Also, it is intended to contribute to the literature of soft set by gaining the relationships between this new soft set operation and some other types of soft set operations via examining the distribution of complementary soft binary piecewise lambda operation over extended soft set operations, complementary extended soft set operations, soft binary piecewise operations, complementary soft binary piecewise operations and restricted soft set operations in order to inspire to obtain the algebaric structures of soft sets and some new decision making methods.

Anahtar Kelimeler

Soft sets, soft set operations, conditional complements

Proje Numarası

YOK

Kaynakça

• Molodtsov, D. (1999). Soft set theory-first results. Computers and Mathematics with Applications, 37(1), 19-31. https://doi.org/10.1016/S0898/1221(99)00056/5
• Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers and Mathematics with Applications, 45(1), 555-562. https://doi.org/10.1016/S08986/1221(03)000166/6
• Pei, D., & Miao, D. (2005). From soft sets to information systems. IEEE International Conference on Granular Computing, (2) 617-621. doi: 10.1109/GRC.2005.1547365.
• Ali, M. I., Feng, F., Liu, X., Min, W. K., & Shabir M. (2009). On some new operations in soft set theory. Computers and Mathematics with Applications, 57(9), 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.00
• Sezgin, A., & Atagün A. O. (2011). On operations of soft sets. Computers and Mathematics with Applications, 61(5), 1457-1467. https://doi.org/10.1016/j.camwa.2011.01.018
• Sezgin, A., Shahzad, A., & Mehmood A. (2019). New operation on soft sets: extended difference of soft sets. Journal of New Theory, (27), 33-42.
• Stojanovic, N. S. (2021). A new operation on soft sets: extended symmetric difference of soft sets. Military Technical Courier, 69(4), 779-791. https://doi.org/10.5937/vojtehg69/33655
• Çağman, N. (2021). Conditional complements of sets and their application to group theory. Journal of New Results in Science, 10(3), 67-74. https://doi.org/10.54187/jnrs.1003890
• Sezgin, A., Çağman, N., Atagün, A. O., & Aybek, F. (2023a). Complemental binary operations of sets and their application to group theory. Matrix Science Mathematic, 2(7), 99-106, https://doi.org/10.26480/msmk.02.2023.99.106
• Aybek, F. (2023). New restricted and extended soft set operations. (unpublished thesis) [Master of Science Thesis, Amasya University].
• Demirci, A. M. (2023). New type of extended operations of soft set: Complementary extended plus, union and theta operations. (unpublished thesis) [Master of Science Thesis, Amasya University].
• Sarıalioğlu, M. (2023). New type of extended operations of soft set: Complementary extended gamma, intersection and star operations. (unpublished thesis) [Master of Science Thesis, Amasya University].
• Akbulut, E. (2023). New type of extended operations of soft set: Complementary extended lambda and difference operations. (unpublished thesis) [Master of Science Thesis, Amasya University].
• Eren, Ö. F. (2019). On soft set theory. (Thesis no: 579410) [Master of Science Thesis, Ondokuz Mayıs University].
• Yavuz, E. (2023). Soft binary piecewise operations and their properties. (unpublished thesis) [Master of Science Thesis, Amasya University].
• Sezgin, A., & Sarıalioğlu, M. (2023). New soft set operation: Complementary soft binary piecewise theta operation. in press in Journal of Kadirli Faculty of Applied Sciences.
• Sezgin, A., & Demirci, A. M. (2023). New soft set operation: Complementary soft binary piecewise star operation. Ikonion Journal of Mathematics, 5(2), 24-52. https://doi.org/10.54286/ikjm.1304566
• Sezgin, A., & Atagün, A. O. (2023). New soft set operation: Complementary soft binary piecewise plus operation. in press in Information Management and Computer Science.
• Sezgin, A., & Çağman, N. (2023). 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.
• Sezgin, A., & Aybek, F. (2023), New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic, 7(1), 27-45. https://doi.org/10.26480/msmk.01.2023.27.45
• Sezgin, A., Aybek, F., & Güngör, N. B. (2023b). New soft set operation: Complementary soft binary piecewise intersection and union operation. Acta Informatica Malaysia, 7(1), 38-53. https://doi.org/10.26480/aim.01.2023.38.53
• Sezgin, A., Aybek, F. & Atagün, A. O. (2023c). New soft set operation: Complementary soft binary piecewise intersection operation. Black Sea Journal of Engineering and Science, 6(4), 330-346. https://doi.org/10.34248/bsengineering.1319873.
• Ali, M. I., Shabir, M., Naz, M. (2011). Algebraic structures of soft sets associated with new operations. Computers and Mathematics with Applications, 61, 2647–2654. https://doi/10.1016/j.camwa.2011.03.011.
• Howie, J. M. (1995). Fundamentals of semigroup theory, Oxford University Press.
• Kilp, M., Knauer, U., & Mikhalev, A. (2001). Monoids, Acts And Categories. De Gruyter Expositions in Mathematics, (29), https://doi.org/10.1515/9783110812909