A COMPREHENSIVE STUDY ON SOFT BINARY PIECEWISE DIFFERENCE OPERATION

Yıl 2024, , 32 - 54, 27.02.2024

Aslıhan Sezgin , Hamza Çalışıcı

https://doi.org/10.20290/estubtdb.1356881

Cited By: 4

Öz

Soft set theory, developed by Molodtsov, has been applied both theoretically and practically in many fields. It is a useful mathematical tool for handling uncertainty. Numerous variations of soft set operations, which is a crucial concept for the theory, have been described and used since its introduction. In this paper, we explore more about soft binary piecewise difference operation (defined first as “difference of soft sets”) and its whole properties are examined especially in comparison with the basic properties of difference operation in classical set theory. Several striking properties of soft binary piecewise operations are obtained as analogous to the characteristic of difference operation in classical set theory. Also, we show that the collection of all soft sets with a fixed parameter set together with the soft binary piecewise difference operation is a bounded BCK-algebra.

Anahtar Kelimeler

soft sets, soft set operations, soft binary piecewise difference operation

Proje Numarası

YOK

ESNEK İKİLİ PARÇALI FARK İŞLEMİNE KAPSAMLI BİR BAKIŞ

Öz

Molodtsov tarafından geliştirilen esnek küme teorisi hem teorik hem de pratik olarak birçok alanda uygulanmıştır. Bu teori, belirsizliği ele almak için yararlı bir matematiksel araçtır. Teori için çok önemli bir kavram olan esnek küme işlemlerinin çok sayıda varyasyonu, teorinin ortaya atılmasından bu yana tanımlanmış ve kullanılmıştır. Bu çalışmada, esnek ikili parçalı fark işlemi (ilk olarak "esnek kümelerin farkı" olarak tanımlanan) hakkında daha fazla bilgi elde edip, bu işlemin tüm özellikleri, özellikle klasik küme teorisindeki fark işleminin temel özellikleriyle karşılaştırmalı olarak incelenecektir. Esnek ikili parçalı işlemlerin birçok çarpıcı özelliği, klasik küme teorisindeki fark işleminin karakteristiğine benzer şekilde elde edilmiştir. Ayrıca, esnek ikili parçalı fark işleminin sabit parametreye sahip esnek kümeler kümesi üzerinde sınırlı bir BCK-cebiri olduğu gösterilmiştir.

Anahtar Kelimeler

ESNEK KÜMELER, ESNEK KÜME İŞLEMLERİ, ESNEK İKİLİ PARÇALI FARK İŞLEMİ

Destekleyen Kurum

YOK

Proje Numarası

YOK

Teşekkür

YOK

Kaynakça

• [1] Molodtsov D. Soft set theory-first results. Comput Math Appl 1999; 37 (1): 19-31.
• [2] Maji PK, Biswas R, Roy, AR. Soft set theory. Comput Math Appl 2003; 45 (1): 555-562.
• [3] Pei D, Miao D. From soft sets to information systems. In: Proceedings of Granular Computing. IEEE 2005; 2: 617-621.
• [4] 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.
• [5] Sezgin A, Atagün AO. On operations of soft sets. Comput Math Appl 2011; 61(5):1457-1467.
• [6] Sezgin A, Shahzad A, Mehmood A. New operation on soft sets: Extended difference of soft sets. J New Theory 2019; (27): 33-42.
• [7] Stojanovic NS. A new operation on soft sets: Extended symmetric difference of soft sets. Military Technical Courier 2021; 69(4): 779-791.
• [8] Yavuz E. Soft binary piecewise operations and their properties. MSc, Amasya University, Amasya, Turkey, 2024.
• [9] Akbulut E. New type of extended operations of soft set: Complementary extended difference and lambda operation. MSc, Amasya University, Amasya, Turkey, 2024.
• [10] Ali MI, Shabir M, Naz M. Algebraic structures of soft sets associated with new operations, Comput Math Appl 2011; 61 2647–2654.
• [11] Aybek FN. New restricted and extended soft set operations. MSc, Amasya University, Amasya, Turkey, 2024.
• [12] Demirci AM. New type of extended operations of soft set: Complementary extended union, plus and theta operation. MSc, Amasya University, Amasya, Turkey, 2024.
• [13] Feng F, Li YM, Davvaz B, Ali MI. Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Comput 2010; 14: 899–911.
• [14] Fu L. Notes on soft set operations. ARPN J Eng Appl Sci 2011; 1: 205-208.
• [15] Ge X, Yang S. Investigations on some operations of soft sets, World Academy of Science, Engineering and Technology. 2011; 75: 1113-1116.
• [16] Husain S, Shamsham Km. A study of properties of soft set and its applications, Int Res J Eng Technol. 2018; 5 (1): 363-372.
• [17] Eren ÖF. On soft set theory. MSc, Ondokuz Mayıs University, Samsun, Turkey, 2019.
• [18] Jayanta S. On algebraic structure of soft sets, Ann Fuzzy Math 2014; 7 (6): 1013-1020.
• [19] Jiang J, Tang Y, Chen Q, Wang J, Tang S. Extending soft sets with description logics, Comput Math Appl 2010; 59: 2087–2096.
• [20] Neog IJ, Sut DK. A new approach to the theory of soft set. Int J Comput Appl. 2011; 32 (2): 1-6.
• [21] Onyeozili LA, Gwary TA. A study of the fundamentals of soft set theory. Int J Sci Technol Res 2014; 3 (4): 132-143.
• [22] Ping Z, Qiaoyan W. Operations on soft sets sevisited, J Appl Math 2013; Volume 2013 Article ID 105752: 7 pages.
• [23] Sarıalioğlu M. New type of extended operations of soft set: Complementary extended intersection, gamma and star operation. MSc, Amasya University, Amasya, Turkey, 2024.
• [24] Sezgin A, Atagün AO. New soft set operation: Complementary soft binary piecewise plus operation. Matrix Science Mathematic 2023; 7 (2) 125-142.
• [25] Sezgin A, Aybek FN. New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic 2023; (7) 1: 27-45.
• [26] Sezgin A, Aybek FN, Güngör N.B. New soft set operation: Complementary soft binary piecewise union operation. Acta Informatica Malaysia 2023a; 7(1): 38-53.
• [27] Sezgin A, Aybek FN, Atagün AO. New soft set operation: Complementary soft binary piecewise intersection operation. BSJ Eng Sci 2023b; 6 (4): 330-346.
• [28] Sezgin A, Çağman N. New soft set operation: Complementary soft binary piecewise difference operation. Osmaniye Korkut Ata Üniv Fen Biliml Derg 2024; 7 (1): 58-94.
• [29] Sezgin A, Demirci AM. New soft set operation: Complementary soft binary piecewise star operation. Ikonion Journal of Mathematics, 2023c; 5 (2): 24-52.
• [30] Sezgin A, Sarıalioğlu M. New soft set operation: Complementary soft binary piecewise theta operation. Journal of Kadirli Faculty of Applied Sciences (in press).
• [31] Singh D, Onyeozili LA. Some conceptual misunderstanding of the fundamentals of soft set theory, ARPN J Eng Appl Sci 2012a; 2 (9): 251-254
• [32] Singh D, Onyeozili LA. Some results on Distributive and absorption properties on soft operations, IOSR J Math 2012b; 4 (2): 18-30.
• [33] Singh D, Onyeozili LA. On some new properties on soft set operations, Int J Comput Appl 2012c; 59 (4): 39-44.
• [34] Singh D, Onyeozili LA. Notes on soft matrices operations, ARPN J Eng Appl Sci 2012d; 2(9): 861-869.
• [35] Yang CF. “A note on: “Soft set theory” [Computers & Mathematics with Applications 45 (2003), no. 4-5, 555–562],” Comput Math Appl 2008; 56 (7) :1899–1900.
• [36] Çağman N. Conditional complements of sets and their application to group theory. J New Results Sci 2021; 10 (3): 67-74.
• [37] Imai Y, Iseki K. On axiom systems of proposition calculi, Proc Jpn Acad, 1966; 42: 19–22.
• [38] Qin K, Hong Z. On soft equality, J Comput Appl Math 2010; 234 (5): 1347–1355.
• [39] Polat N, Yaylalı Umul G, Tanay B. On soft ring and soft topological ring. Eskişehir Teknik Univ Bilim Teknol Derg Teor Bilim 2023; 11 (2): 148-157.