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A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation

Yıl 2023, Cilt: 5 Sayı: 2, 189 - 208, 31.12.2023

Aslıhan Sezgin Eda Yavuz

https://doi.org/10.47112/neufmbd.2023.18

Öz

The soft set theory developed by Molodtsov has been applied both theoretically and practically in many fields. It is a useful piece of mathematics for handling uncertainty. Numerous variations of soft set operations have been described and used since its introduction. In this paper, a new soft set operation, called soft binary piecewise symmetric difference operation, is defined, its properties are considered and examined comparatively with the basic algebraic properties of symmetric difference operation existing in classical set theory. Moreover, we prove that the set of all the soft sets with a fixed parameter set together with the soft binary piecewise symmetric difference operation and the restricted intersection operation is a commutative hemiring with identity and also Boolean ring.

Anahtar Kelimeler

Soft Sets Soft Sets Operations Boolen Rings Hemirings

Destekleyen Kurum

YOK

Proje Numarası

YOK

Teşekkür

POTENTIAL REVIEWERS ARE: 1) Faruk Karaaslan, fkaraaslan@karatekin.edu.tr, Çankırı Karatekin Üniversitesi 2) Akın Osman Atagün, Yozgat Bozok University, aosman.atagun@ahievran.edu.tr 3)Muhammad Riaz, University of the Punjab , mriaz.math@pu.edu.pk 4)Murat Lüzum, Van Yüzüncü Yıl Üniversitesi, mluzum@yyu.edu.tr 5) Şerif Özlü, Gaziantep üniversitesi, serif.ozlu@hotmail.com

Kaynakça

  • D. Molodtsov, Soft set theory-first results. Computers and Mathematics with Applications. 37 (1) (1999), 19-31. doi:10.1016/S0898/1221(99)00056/5
  • P.K. Maji, R. Bismas, A.R. Roy, Soft set theory, Computers and Mathematics with Applications. 45 (1) (2003), 555-562. doi:10.1016/S08986/1221(03)000166/6
  • D. Pei and D. Miao, From Soft Sets to Information Systems, In: Proceedings of Granular Computing. IEEE. 2 (2005), 617-621. doi: 10.1109/GRC.2005.1547365
  • 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) (2009), 1547-1553. doi:10.1016/j.camwa.2008.11.00
  • A. Sezgin, A. O. Atagün, On operations of soft sets, Computers and Mathematics with Applications. 61(5) (2011), 1457-1467. doi:10.1016/j.camwa.2011.01.018
  • A. Sezgin, A. Shahzad, A. Mehmood A. New Operation on Soft Sets: Extended Difference of Soft Sets, Journal of New Theory. (27) (2019), 33-42.
  • N. S. Stojanovic, A new operation on soft sets: extended symmetric difference of soft sets, Military Technical Courier. 69(4) (2021), 779-791. doi:10.5937/vojtehg69/33655
  • Ö. F. Eren, On operations of soft sets, Master of Science Thesis, Ondokuz Mayıs University, The Graduate School of Natural and Applied Sciences in Mathematics Department, Samsun, 2019.
  • E. Yavuz, Soft binary piecewise operations and their properties, Master of Science Thesis, Amasya University, The Graduate School of Natural and Applied Sciences in Mathematics Department, Amasya, 2024.
  • A. Sezgin, M. Sarıalioğlu M., New soft set operation: Complementary soft binary piecewise theta operation, Journal of Kadirli Faculty of Applied Sciences. (in press).
  • A. Sezgin F. Aybek, A.O. Atagün, New soft set operation: Complementary soft binary piecewise intersection operation, Black Sea Journal of Engineering and Science. (6)4 (2023), 330-346. doi:10.34248/bsengineering.1319873
  • A. Sezgin, F. Aybek, N. B. Güngör, New soft set operation: Complementary soft binary piecewise union operation, Acta Informatica Malaysia. (7)1 (2023), 38-53. doi:10.26480/aim.01.2023.38.53
  • 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. (in press).
  • C.F. Yang, “A note on: “Soft set theory” [Computers & Mathematics with Applications 45 (2003), 4-5, 555–562],” Computers & Mathematics with Applications. 56 (7) (2008), 1899–1900. doi:10.1016/j.camwa.2008.03.019
  • F. Feng, Y. M. Li, B. Davvaz, M.I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing. 14 (2010), 899–911. doi:10.1007/s00500-009-0465-6
  • Y. Jiang, Y. Tang, Q. Chen, J. Wang, S. Tang, Extending soft sets with description logics, Computers and Mathematics with Applications. 59 (2010), 2087–2096. doi:10.1016/j.camwa.2009.12.014
  • M.I. Ali, M. Shabir, M. Naz, Algebraic structures of soft sets associated with new operations, Computers and Mathematics with Applications. 61 (2011), 2647–2654. doi:10.1016/j.camwa.2011.03.011
  • I.J. Neog, D.K. Sut, A new approach to the theory of soft set, International Journal of Computer Applications, 32 (2) (2011), 1-6. doi:10.5120/3874-5415
  • L. Fu, Notes on soft set operations, ARPN Journal of Systems And Softwares, 1 (2011), 205-208. doi:10.1142/9789814365147_0008
  • X. Ge, S. Yang, Investigations on some operations of soft sets, World Academy of Science, Engineering and Technology, 75 (2011), 1113-1116
  • D. Singh, I.A. Onyeozili, Some conceptual misunderstanding of the fundamentals of soft set theory, ARPN Journal of Systems and Softwares, 2 (9) (2012a), 251-254.
  • D. Singh, I.A. Onyeozili, Some results on Distributive and absorption properties on soft operations, IOSR Journal of Mathematics, 4 (2) (2012b), 18-30.
  • D. Singh, I.A. Onyeozili, On some new properties on soft set operations, International Journal of Computer Applications. 59 (4) (2012c), 39-44.
  • D. Singh, I.A. Onyeozili, Notes on soft matrices operations, ARPN Journal of Science and Technology. 2(9) (2012d), 861-869.
  • Z. Ping, W. Qiaoyan, Operations on soft sets revisited, Journal of Applied Mathematics. Volume 2013 Article ID 105752 (2013), 7 pages. doi:10.1155/2013/105752
  • S. Jayanta, On algebraic structure of soft sets, Annals of Fuzzy Mathematics and Informatics. 7 (6) (2014), 1013-1020.
  • I.A. Onyeozili, T.M. Gwary, A study of the fundamentals of soft set theory, Internatıonal Journal of Scıentıfıc & Technology Research. 3 (4) (2014), 132-143.
  • S. Husain, Km. Shamsham, A study of properties of soft set and its applications, International Research Journal of Engineering and Technology. 5 (1) (2018), 363-372.
  • H. S. Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold, Bulletin of the American Mathematical Society. 40 (12) (1934), 914–920. doi:10.1090/S0002-9904-1934-06003-8
  • T. Vasanthi and N. Sulochana, On the additive and multiplicative structure of semirings, Annals of Pure and Applied Mathematics. 3 (1) (2013), 78–84.
  • A. Kaya and M. Satyanarayana, Semirings satisfying properties of distributive type, Proceedings of the American Mathematical Society. 82 (3) (1981), 341–346. doi:10.2307/2043936
  • P. H. Karvellas, Inversive semirings, Journal of the Australian Mathematical Society, (18) 3 (1974), 277–288. doi:10.1017/S1446788700022850
  • K. R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
  • M. Petrich, Introduction to Semiring, Charles E Merrill Publishing Company, Ohio, 1973.
  • C. Reutenauer and H. Straubing, Inversion of matrices over a commutative semiring, Journal of Algebra. 88 (2) (1984), 350–360. doi:10.1016/0021-8693(84)90070-X
  • K. Glazek, A guide to litrature on semirings and their applications in mathematics and ınformation sciences: with complete bibliography, Kluwer Academiy Publication, Nederland, 2002.
  • L. B. Beasley, N.G. Pullman, Operators that preserves semiring matrix functions, Linear Algebra Application. 99 (1988), 199–216. doi:10.1016/0024-3795(88)90132-2
  • L.B. Beasley, N.G. Pullman, Linear operators strongly preserving idempotent matrices over semirings, Linear Algebra Appliction. 160 (1992), 217–229. doi:10.1016/0024-3795(92)90448-J
  • S. Ghosh, Matrices over semirings, Information Science. 90 (1996), 221–230. doi:10.1016/0020-0255(95)00283-9.
  • W. Wechler, The concept of fuzziness in automata and language theory, Akademic Verlag, Berlin, 1978.
  • J. S. Golan, Semirings and their applications, Springer Dordrecht, 1999. https://doi:10.1007/978-94-015-9333-5.
  • U. Hebisch, H.J. Weinert, Semirings: Algebraic theory and applications in the computer science, World Scientific, Germany, 1998.

Yeni Bir Esnek Küme İşlemi: Esnek İkili Parçalı Simetrik Fark İşlemi

Yıl 2023, Cilt: 5 Sayı: 2, 189 - 208, 31.12.2023

Aslıhan Sezgin Eda Yavuz

https://doi.org/10.47112/neufmbd.2023.18

Öz

Molodtsov tarafından geliştirilen esnek küme teorisi hem teorik hem de pratik olarak birçok alanda uygulanmıştır. Belirsizliği ele almak için yararlı bir matematiksel araçtır. Ortaya atıldığından bu yana çok sayıda esnek küme işlemi varyasyonu tanımlanmış ve kullanılmıştır. Bu çalışmada, esnek ikili parçalı simetrik fark işlemi adı verilen yeni bir esnek küme işlemi tanımlanıp, özellikleri klasik küme teorisinde var olan simetrik fark işleminin temel cebirsel özellikleri ile karşılaştırmalı olarak ele alınmış ve incelenmiştir. Ayrıca, esnek ikili parçalı simetrik fark işlemi ve kısıtlanmıs kesisim işlemleri ile birlikte sabit parametreye sahip tüm esnek kümelerin oluşturduğu cebirsel yapının, birimli ve değişmeli bir hemiring ve ayrıca Boole halkası olduğu gösterilmiştir.

Anahtar Kelimeler

Esnek Kümeler Esnek Küme İşlemleri Bool Halkası Hemiring

Proje Numarası

YOK

Kaynakça

  • D. Molodtsov, Soft set theory-first results. Computers and Mathematics with Applications. 37 (1) (1999), 19-31. doi:10.1016/S0898/1221(99)00056/5
  • P.K. Maji, R. Bismas, A.R. Roy, Soft set theory, Computers and Mathematics with Applications. 45 (1) (2003), 555-562. doi:10.1016/S08986/1221(03)000166/6
  • D. Pei and D. Miao, From Soft Sets to Information Systems, In: Proceedings of Granular Computing. IEEE. 2 (2005), 617-621. doi: 10.1109/GRC.2005.1547365
  • 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) (2009), 1547-1553. doi:10.1016/j.camwa.2008.11.00
  • A. Sezgin, A. O. Atagün, On operations of soft sets, Computers and Mathematics with Applications. 61(5) (2011), 1457-1467. doi:10.1016/j.camwa.2011.01.018
  • A. Sezgin, A. Shahzad, A. Mehmood A. New Operation on Soft Sets: Extended Difference of Soft Sets, Journal of New Theory. (27) (2019), 33-42.
  • N. S. Stojanovic, A new operation on soft sets: extended symmetric difference of soft sets, Military Technical Courier. 69(4) (2021), 779-791. doi:10.5937/vojtehg69/33655
  • Ö. F. Eren, On operations of soft sets, Master of Science Thesis, Ondokuz Mayıs University, The Graduate School of Natural and Applied Sciences in Mathematics Department, Samsun, 2019.
  • E. Yavuz, Soft binary piecewise operations and their properties, Master of Science Thesis, Amasya University, The Graduate School of Natural and Applied Sciences in Mathematics Department, Amasya, 2024.
  • A. Sezgin, M. Sarıalioğlu M., New soft set operation: Complementary soft binary piecewise theta operation, Journal of Kadirli Faculty of Applied Sciences. (in press).
  • A. Sezgin F. Aybek, A.O. Atagün, New soft set operation: Complementary soft binary piecewise intersection operation, Black Sea Journal of Engineering and Science. (6)4 (2023), 330-346. doi:10.34248/bsengineering.1319873
  • A. Sezgin, F. Aybek, N. B. Güngör, New soft set operation: Complementary soft binary piecewise union operation, Acta Informatica Malaysia. (7)1 (2023), 38-53. doi:10.26480/aim.01.2023.38.53
  • 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. (in press).
  • C.F. Yang, “A note on: “Soft set theory” [Computers & Mathematics with Applications 45 (2003), 4-5, 555–562],” Computers & Mathematics with Applications. 56 (7) (2008), 1899–1900. doi:10.1016/j.camwa.2008.03.019
  • F. Feng, Y. M. Li, B. Davvaz, M.I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing. 14 (2010), 899–911. doi:10.1007/s00500-009-0465-6
  • Y. Jiang, Y. Tang, Q. Chen, J. Wang, S. Tang, Extending soft sets with description logics, Computers and Mathematics with Applications. 59 (2010), 2087–2096. doi:10.1016/j.camwa.2009.12.014
  • M.I. Ali, M. Shabir, M. Naz, Algebraic structures of soft sets associated with new operations, Computers and Mathematics with Applications. 61 (2011), 2647–2654. doi:10.1016/j.camwa.2011.03.011
  • I.J. Neog, D.K. Sut, A new approach to the theory of soft set, International Journal of Computer Applications, 32 (2) (2011), 1-6. doi:10.5120/3874-5415
  • L. Fu, Notes on soft set operations, ARPN Journal of Systems And Softwares, 1 (2011), 205-208. doi:10.1142/9789814365147_0008
  • X. Ge, S. Yang, Investigations on some operations of soft sets, World Academy of Science, Engineering and Technology, 75 (2011), 1113-1116
  • D. Singh, I.A. Onyeozili, Some conceptual misunderstanding of the fundamentals of soft set theory, ARPN Journal of Systems and Softwares, 2 (9) (2012a), 251-254.
  • D. Singh, I.A. Onyeozili, Some results on Distributive and absorption properties on soft operations, IOSR Journal of Mathematics, 4 (2) (2012b), 18-30.
  • D. Singh, I.A. Onyeozili, On some new properties on soft set operations, International Journal of Computer Applications. 59 (4) (2012c), 39-44.
  • D. Singh, I.A. Onyeozili, Notes on soft matrices operations, ARPN Journal of Science and Technology. 2(9) (2012d), 861-869.
  • Z. Ping, W. Qiaoyan, Operations on soft sets revisited, Journal of Applied Mathematics. Volume 2013 Article ID 105752 (2013), 7 pages. doi:10.1155/2013/105752
  • S. Jayanta, On algebraic structure of soft sets, Annals of Fuzzy Mathematics and Informatics. 7 (6) (2014), 1013-1020.
  • I.A. Onyeozili, T.M. Gwary, A study of the fundamentals of soft set theory, Internatıonal Journal of Scıentıfıc & Technology Research. 3 (4) (2014), 132-143.
  • S. Husain, Km. Shamsham, A study of properties of soft set and its applications, International Research Journal of Engineering and Technology. 5 (1) (2018), 363-372.
  • H. S. Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold, Bulletin of the American Mathematical Society. 40 (12) (1934), 914–920. doi:10.1090/S0002-9904-1934-06003-8
  • T. Vasanthi and N. Sulochana, On the additive and multiplicative structure of semirings, Annals of Pure and Applied Mathematics. 3 (1) (2013), 78–84.
  • A. Kaya and M. Satyanarayana, Semirings satisfying properties of distributive type, Proceedings of the American Mathematical Society. 82 (3) (1981), 341–346. doi:10.2307/2043936
  • P. H. Karvellas, Inversive semirings, Journal of the Australian Mathematical Society, (18) 3 (1974), 277–288. doi:10.1017/S1446788700022850
  • K. R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
  • M. Petrich, Introduction to Semiring, Charles E Merrill Publishing Company, Ohio, 1973.
  • C. Reutenauer and H. Straubing, Inversion of matrices over a commutative semiring, Journal of Algebra. 88 (2) (1984), 350–360. doi:10.1016/0021-8693(84)90070-X
  • K. Glazek, A guide to litrature on semirings and their applications in mathematics and ınformation sciences: with complete bibliography, Kluwer Academiy Publication, Nederland, 2002.
  • L. B. Beasley, N.G. Pullman, Operators that preserves semiring matrix functions, Linear Algebra Application. 99 (1988), 199–216. doi:10.1016/0024-3795(88)90132-2
  • L.B. Beasley, N.G. Pullman, Linear operators strongly preserving idempotent matrices over semirings, Linear Algebra Appliction. 160 (1992), 217–229. doi:10.1016/0024-3795(92)90448-J
  • S. Ghosh, Matrices over semirings, Information Science. 90 (1996), 221–230. doi:10.1016/0020-0255(95)00283-9.
  • W. Wechler, The concept of fuzziness in automata and language theory, Akademic Verlag, Berlin, 1978.
  • J. S. Golan, Semirings and their applications, Springer Dordrecht, 1999. https://doi:10.1007/978-94-015-9333-5.
  • U. Hebisch, H.J. Weinert, Semirings: Algebraic theory and applications in the computer science, World Scientific, Germany, 1998.
Toplam 42 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematiksel Mantık, Kümeler Teorisi, Kafesler ve Evrensel Cebir
Bölüm Makaleler
Yazarlar

Aslıhan Sezgin 0000-0002-1519-7294

Eda Yavuz 0009-0001-4412-422X

Proje Numarası YOK
Erken Görünüm Tarihi 22 Aralık 2023
Yayımlanma Tarihi 31 Aralık 2023
Kabul Tarihi 21 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 5 Sayı: 2

Kaynak Göster

APA Sezgin, A., & Yavuz, E. (2023). A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 5(2), 189-208. https://doi.org/10.47112/neufmbd.2023.18
AMA Sezgin A, Yavuz E. A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation. NEU Fen Muh Bil Der. Aralık 2023;5(2):189-208. doi:10.47112/neufmbd.2023.18
Chicago Sezgin, Aslıhan, ve Eda Yavuz. “A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 5, sy. 2 (Aralık 2023): 189-208. https://doi.org/10.47112/neufmbd.2023.18.
EndNote Sezgin A, Yavuz E (01 Aralık 2023) A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5 2 189–208.
IEEE A. Sezgin ve E. Yavuz, “A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation”, NEU Fen Muh Bil Der, c. 5, sy. 2, ss. 189–208, 2023, doi: 10.47112/neufmbd.2023.18.
ISNAD Sezgin, Aslıhan - Yavuz, Eda. “A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation”. Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 5/2 (Aralık 2023), 189-208. https://doi.org/10.47112/neufmbd.2023.18.
JAMA Sezgin A, Yavuz E. A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation. NEU Fen Muh Bil Der. 2023;5:189–208.
MLA Sezgin, Aslıhan ve Eda Yavuz. “A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation”. Necmettin Erbakan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 5, sy. 2, 2023, ss. 189-08, doi:10.47112/neufmbd.2023.18.
Vancouver Sezgin A, Yavuz E. A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation. NEU Fen Muh Bil Der. 2023;5(2):189-208.
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