A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation

Aslıhan Sezgin; Naim Cagman

doi:10.47495/okufbed.1308379

Araştırma Makalesi

Yeni Bir Esnek Küme İşlemi: Tümleyenli Esnek İkili Parçalı Fark (\) İşlemi

Yıl 2024, Cilt: 7 Sayı: 1, 58 - 94, 22.01.2024

Aslıhan Sezgin Naim Cagman

https://doi.org/10.47495/okufbed.1308379

Cited By: 1

Öz

Esnek küme teorisi, belirsizlikle başa çıkan bir teoridir. Başlangıcından bu yana, birçok türde esnek küme işlemi tanımlanmış ve çeşitli türlerde kullanılmıştır. Bu çalışmada, tümleyenli esnek ikili parçalı fark işlemi adı verilen yeni bir esnek küme işlemi tanımlanmış ve temel cebirsel özellikleri araştırılmıştır. Klasik teorideki fark işlemi ile esnek küme teorisindeki tümleyenli esnek ikili parçalı fark işlemi arasında birçok çarpıcı benzer özellikler elde edilmiştir. Ayrıca bu işlem ile diğer tüm esnek küme işlemleri arasındaki ilişkiler dağılma kurallar yardımıyla incelenerek, esnek küme literatürüne katkıda bulunma amaçlanmıştır.

Anahtar Kelimeler

esnek küme, esnek küme işlemleri, şartlı tümleyen

Proje Numarası

-

Kaynakça

Addis GM., Engidaw DA., Davvaz B. Soft mappings: a new approach. Soft Computing 2022; 26: 3589-3599.
Ali MI., Feng F., Liu X., Min WK., Shabir M. On some new operations in soft set theory. Computers and Mathematics with Applications 2009; 57(9): 1547-1553.
Atagün AO., Aygün E. Groups of soft sets. Journal of Intelligent & Fuzzy Systems 2016; 30: 729-733.
Ayub S., Shabir M., Riaz M., Aslam M., Chinram R. Linear diophantine fuzzy relations and their algebraic properties with decision making. Symmetry 2021: 13(6): 945.
Eren ÖF., Çalışıcı H. On some operations of soft sets. The Fourth International Conference on Computational Mathematics and Engineering Sciences (CMES-2019), 20-22 April 2019, Antalya.
Çağman N. Conditional complements of sets and their application to group theory. Journal of New Results in Science 2021; 10(3): 67-74.
Molodtsov D. Soft set theory-first results. Computers and Mathematics with Applications 1999; 37 (1): 19-31.
Maji PK., Bismas R., Roy AR. Soft set theory. Computers and Mathematics with Applications 2003; 45(1): 555-562.
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.
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.
Paik B, Mondal, SK. Introduction to soft-cryptosystem and its application. Wireless Personal Communications 2022; 125: 1801–1826.
Pei D., Miao D. From soft sets to ınformation systems. Proceedings of IEEE Granular Computing 2005; 2: 617-621.
Riaz M., Hashmi MR. Linear diophantine fuzzy set and its applications towards multi-attribute decision-making problems. Journal of Intelligent and Fuzzy Systems 2019; 37: 5417-5439.
Riaz M., Farid HMA. Linear diophantine fuzzy aggregation operators with multi-criteria decision-making. Journal of Computational and Cognitive Engineering 2023; 1–12.
Riaz M., Hashmi MR., Pamucar D., Chu Y. Spherical linear diophantine fuzzy sets with modeling uncertainties in MCDM. Computer Modeling in Engineering and Sciences 2021; 126: 1125-1164.
Sezgin A., Atagün AO. On operations of soft sets. Computers and Mathematics with Applications 2011; 61(5):1457-1467.
Sezgin A., Shahzad A., Mehmood A. New operation on soft sets: extended difference of soft sets. Journal of New Theory 2019; 27: 33-42.
Sezgin A., Çağman N., Atagün AO., Aybek F. Complemental binary operations of sets and their application to group theory. Unpublished results 2023a.
Sezgin A., Aybek F. New restricted and extended soft set operations. Amasya University Graduate School of Natural and Applied Sciences Master of Science in Mathematics Department, Amasya, 2023a.
Sezgin A., Demirci AM. New type of extended operations of soft set: Complementary extended plus, union and theta operations. Amasya University Graduate School of Natural and Applied Sciences Master of Science in Mathematics Department, Amasya, 2023a.
Sezgin A., Sarıalioğlu, M. New type of extended operations of soft set: Complementary extended gamma, intersection and star operations. Amasya University Graduate School of Natural and Applied Sciences Master of Science in Mathematics Department, Amasya, 2023a.

A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation

Yıl 2024, Cilt: 7 Sayı: 1, 58 - 94, 22.01.2024

Aslıhan Sezgin Naim Cagman

https://doi.org/10.47495/okufbed.1308379

Cited By: 1

Öz

Soft set theory is a theory of dealing with uncertainty. Since its inception, many kinds of soft set operations are defined and used in various types. In this paper, a new kind of soft set operation called, complementary soft binary piecewise difference operation is defined and its basic properties are investigated. We obtain many striking analogous fact between difference operation in classical theory and complementary soft binary piecewise difference operation in soft set theory. Also, by obtaining the relationships between this new soft set operation and all other types of soft set operations, we aim to contribute to the soft set literature with the help of examing the distribution rules.

Anahtar Kelimeler

soft set, soft set operations, conditional complements

Destekleyen Kurum

-

Proje Numarası

-

Teşekkür

-

Kaynakça

Addis GM., Engidaw DA., Davvaz B. Soft mappings: a new approach. Soft Computing 2022; 26: 3589-3599.
Ali MI., Feng F., Liu X., Min WK., Shabir M. On some new operations in soft set theory. Computers and Mathematics with Applications 2009; 57(9): 1547-1553.
Atagün AO., Aygün E. Groups of soft sets. Journal of Intelligent & Fuzzy Systems 2016; 30: 729-733.
Ayub S., Shabir M., Riaz M., Aslam M., Chinram R. Linear diophantine fuzzy relations and their algebraic properties with decision making. Symmetry 2021: 13(6): 945.
Eren ÖF., Çalışıcı H. On some operations of soft sets. The Fourth International Conference on Computational Mathematics and Engineering Sciences (CMES-2019), 20-22 April 2019, Antalya.
Çağman N. Conditional complements of sets and their application to group theory. Journal of New Results in Science 2021; 10(3): 67-74.
Molodtsov D. Soft set theory-first results. Computers and Mathematics with Applications 1999; 37 (1): 19-31.
Maji PK., Bismas R., Roy AR. Soft set theory. Computers and Mathematics with Applications 2003; 45(1): 555-562.
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.
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.
Paik B, Mondal, SK. Introduction to soft-cryptosystem and its application. Wireless Personal Communications 2022; 125: 1801–1826.
Pei D., Miao D. From soft sets to ınformation systems. Proceedings of IEEE Granular Computing 2005; 2: 617-621.
Riaz M., Hashmi MR. Linear diophantine fuzzy set and its applications towards multi-attribute decision-making problems. Journal of Intelligent and Fuzzy Systems 2019; 37: 5417-5439.
Riaz M., Farid HMA. Linear diophantine fuzzy aggregation operators with multi-criteria decision-making. Journal of Computational and Cognitive Engineering 2023; 1–12.
Riaz M., Hashmi MR., Pamucar D., Chu Y. Spherical linear diophantine fuzzy sets with modeling uncertainties in MCDM. Computer Modeling in Engineering and Sciences 2021; 126: 1125-1164.
Sezgin A., Atagün AO. On operations of soft sets. Computers and Mathematics with Applications 2011; 61(5):1457-1467.
Sezgin A., Shahzad A., Mehmood A. New operation on soft sets: extended difference of soft sets. Journal of New Theory 2019; 27: 33-42.
Sezgin A., Çağman N., Atagün AO., Aybek F. Complemental binary operations of sets and their application to group theory. Unpublished results 2023a.
Sezgin A., Aybek F. New restricted and extended soft set operations. Amasya University Graduate School of Natural and Applied Sciences Master of Science in Mathematics Department, Amasya, 2023a.
Sezgin A., Demirci AM. New type of extended operations of soft set: Complementary extended plus, union and theta operations. Amasya University Graduate School of Natural and Applied Sciences Master of Science in Mathematics Department, Amasya, 2023a.
Sezgin A., Sarıalioğlu, M. New type of extended operations of soft set: Complementary extended gamma, intersection and star operations. Amasya University Graduate School of Natural and Applied Sciences Master of Science in Mathematics Department, Amasya, 2023a.

Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Araştırma Makaleleri (RESEARCH ARTICLES)
Yazarlar	Aslıhan Sezgin Naim Cagman 0000-0003-3037-1868
Proje Numarası	-
Yayımlanma Tarihi	22 Ocak 2024
Gönderilme Tarihi	1 Haziran 2023
Kabul Tarihi	26 Temmuz 2023
Yayımlandığı Sayı	Yıl 2024 Cilt: 7 Sayı: 1

Kaynak Göster

APA	Sezgin, A., & Cagman, N. (2024). A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 7(1), 58-94. https://doi.org/10.47495/okufbed.1308379
AMA	Sezgin A, Cagman N. A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). Ocak 2024;7(1):58-94. doi:10.47495/okufbed.1308379
Chicago	Sezgin, Aslıhan, ve Naim Cagman. “A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7, sy. 1 (Ocak 2024): 58-94. https://doi.org/10.47495/okufbed.1308379.
EndNote	Sezgin A, Cagman N (01 Ocak 2024) A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7 1 58–94.
IEEE	A. Sezgin ve N. Cagman, “A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation”, OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci), c. 7, sy. 1, ss. 58–94, 2024, doi: 10.47495/okufbed.1308379.
ISNAD	Sezgin, Aslıhan - Cagman, Naim. “A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7/1 (Ocak 2024), 58-94. https://doi.org/10.47495/okufbed.1308379.
JAMA	Sezgin A, Cagman N. A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). 2024;7:58–94.
MLA	Sezgin, Aslıhan ve Naim Cagman. “A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 7, sy. 1, 2024, ss. 58-94, doi:10.47495/okufbed.1308379.
Vancouver	Sezgin A, Cagman N. A New Soft Set Operation: Complementary Soft Binary Piecewise Difference (\) Operation. OKÜ Fen Bil. Ens. Dergisi ((OKU Journal of Nat. & App. Sci). 2024;7(1):58-94.