Complementary Extended Gamma Operation: A New Soft Set Operation

Yıl 2024, Cilt: 7 Sayı: 1, 15 – 44, 30.06.2024

Aslıhan Sezgin Murat Sarıalioğlu

https://doi.org/10.38061/idunas.1482044

Öz

Kaynakça

  • 1. Molodtsov D. (1999) Soft set theory-first results. Comput Math Appl. 37 (1): 19-31.
  • 2. Maji PK, Biswas R and Roy AR. (2003) Soft set theory. Comput Math Appl. 45 (1): 555-562.
  • 3. Pei D and Miao D. (2005) From soft sets to information systems. In: Proceedings of Granular Computing IEEE, 2: 617-621.
  • 4. Ali MI, Feng F, Liu X, Min WK and Shabir M. (2009) On some new operations in soft set theory. Comput Math Appl,57(9): 1547-1553.
  • 5. Sezgin A and Atagün AO. (2011) On operations of soft sets. Comput Math Appl, 61(5):1457-1467.
  • 6. Ali MI, Shabir M, Naz M. (2011) Algebraic structures of soft sets associated with new operations, Comput Math Appl, 61: 2647–2654.
  • 7. Sezgin A, Shahzad A and Mehmood A.(2019) New operation on soft sets: Extended difference of soft sets. J New Theory, (27): 33-42.
  • 8. Stojanovic NS. (2021) A new operation on soft sets: Extended symmetric difference of soft sets. Military Technical Courier, 69(4): 779-791.
  • 9. Eren ÖF and Çalışıcı H. (2019) On some operations of soft sets, The Fourth International Conference on Computational Mathematics and Engineering Sciences, Antalya.
  • 10. Sezgin A and Çalışıcı H. (2024) A comprehensive study on soft binary piecewise difference operation. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B-Teorik Bilimler, 12 (1): 32-54.
  • 11. Çağman N. (2021) Conditional complements of sets and their application to group theory. J New Results Sci. 10 (3): 67-74.
  • 12. Sezgin A, Çağman N, Atagün AO and Aybek FN. (2023a) Complemental binary operations of sets and their application to group theory. Matrix Science Mathematic, 7 (2): 114-121.
  • 13. Aybek FN. New restricted and extended soft set operations, MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 14. Sezgin A and Atagün AO. (2023) New soft set operation: Complementary soft binary piecewise plus operation. Matrix Science Mathematic, 7 (2) 125-142.
  • 15. Sezgin A and Aybek FN. (2023) New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic (7) 1: 27-45.
  • 16. Sezgin A, Aybek FN and Güngör N.B. (2023b) New soft set operation: Complementary soft binary piecewise union operation. Acta Informatica Malaysia, 7(1): 38-53.
  • 17. Sezgin A, Aybek FN and Atagün AO. (2023c) New soft set operation: Complementary soft binary piecewise intersection operation. BSJ Eng Sci 6 (4): 330-346.
  • 18. Sezgin A and Çağman N. (2024) New soft set operation: Complementary soft binary piecewise difference operation. Osmaniye Korkut Ata Üniv Fen Biliml Derg, 7 (1): 58-94.
  • 19. Sezgin A and Demirci AM. (2023) New soft set operation: Complementary soft binary piecewise star operation. Ikonion Journal of Mathematics, 5 (2): 24-52.
  • 20. Sezgin A and Sarıalioğlu M. (2024) New soft set operation: Complementary soft binary piecewise theta operation. Journal of Kadirli Faculty of Applied Sciences, 4 (2): 325-357.
  • 21. Sezgin A and Yavuz E. (2023b) New soft set operation: Complementary Soft Binary Piecewise Lambda Operation. Sinop University Journal of Natural Sciences, 8 (2): 101-133.
  • 22. Sezgin A and Dagtoros K. (2023) Complementary soft binary piecewise symmetric difference operation: a novel soft set operation. Scientific Journal of Mehmet Akif Ersoy University, 6(2): 31-45.
  • 23. Akbulut E. New type of extended operations of soft set: Complementary extended difference and lambda operation. MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 24. Demirci AM. New type of extended operations of soft set: Complementary extended union, plus and theta operation. MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 25. Jun, Y. B. and Yang, X. (2011). A note on the paper combination of ınterval-valued fuzzy set and soft set. Comput Math Appl, 61(5): 1468-1470.
  • 26. Liu, X., Feng, F. and Jun, Y. B. (2012). A note on generalized soft equal relations. Comput Math Appl, 64(4): 572-578.
  • 27. Feng, F. and Li, Y. (2013). Soft subsets and soft product operations. Inform Sci, 44-57.
  • 28. Abbas, M., Ali, B. and Romaguera, S. (2014). on generalized soft equality and soft lattice structure. Filomat, 28(6): 1191-1203.
  • 29. Abbas, M., Ali, M.I., Romaguera, S., (2017) Generalized operations in soft set theory via relaxed conditions on parameters, Filomat 31(19): 5955–5964.
  • 30. Al-shami, T.M., (2019) Investigation and corrigendum to some results related to g-soft equality and g f -soft equality relations. Filomat, 33: 3375–3383.
  • 31. Alshasi, T., El-Shafei., T., (2020) T-soft equality relation, Turkish Journal of Mathematics, 44 (4): Article 25.
  • 32. Ali, B., Saleem, N., Sundus, N, Khaleeq, S, Saeed, M., George, R. A., (2022) Contribution to the theory of soft sets via generalized relaxed operations, Mathematics, 10: 26-36.
  • 33. Çağman N, Çitak F and Aktaş H. (2012) Soft int-group and its applications to group theory. Neural Comput Appl. 2: 151–158.
  • 34. Sezgin A and Orbay M. (2022) Analysis of semigroups with soft intersection ideals. Acta Univ Sapientiae Math. 14 (1): 166-210.
  • 35. Mahmood T, Rehman ZU and Sezgin A.(2018) Lattice ordered soft near rings. Korean J Math. 26 (3): 503-517.
  • 36. Jana C, Pal M, Karaaslan F and Sezgin A. (2019) (α, β)-soft intersectional rings and ideals with their applications. New Math Nat Comput. 15 (2): 333–350.
  • 37. Muştuoğlu E, Sezgin A and Türk ZK. (2016) Some characterizations on soft uni-groups and normal soft uni-groups. Int J Comput Appl. 155 (10): 1-8.
  • 38. Sezer AS, Çağman N and Atagün AO. (2015) Uni-soft substructures of groups. Ann Fuzzy Math Inform, 9 (2): 235–246.
  • 39. Sezer AS. (2014) Certain Characterizations of LA-semigroups by soft sets. J Intell Fuzzy Syst, 27 (2): 1035-1046.
  • 40. Özlü Ş and Sezgin A. (2020) Soft covered ideals in semigroups. Acta Univ Sapientiae Math, 12 (2): 317-346.
  • 41. Atagün AO and Sezgin A. (2018) Soft subnear-rings, soft ideals and soft n-subgroups of near-rings. Math Sci Letters, 7 (1): 37-42.
  • 42. Sezgin A. (2018) A new view on AG-groupoid theory via soft sets for uncertainty modeling. Filomat, 32 (8): 2995–3030.
  • 43. Iftikhar M and Mahmood T. (2018) Some results on lattice ordered double framed soft semirings, International Journal of Algebra and Statistics, 7: 123-140.
  • 44. Sezgin A, Çağman N and Atagün AO. (2017) A completely new view to soft intersection rings via soft uni-int product. Appl Soft Comput, 54: 366-392.
  • 45. Mahmood T, Waqas A and Rana M.A. (2015) Soft Intersectional Ideals in Ternary Semirings, Science International, 27 (5): 3929-3934.
  • 46. Sezgin A, Atagün AO and Çağman N and Demir H. (2022) On near-rings with soft union ideals and applications. New Math Nat Comput. 18 (2): 495-511.
  • 47. Yavuz E. Soft binary piecewise operations and their properties. MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 48. Sezgin A and Yavuz E. (2023a) A new soft set operation: Soft binary piecewise symmetric difference operation. Necmettin Erbakan University Journal of Science and Engineering, 5 (2): 189-208.
  • 49. Clifford, A. H. (1954). Bands of semigroups, Proc Am Math Soc, 5(3): 499–504.
  • 50. Kilp M., Knauer U and Mikhalev A. (2001). Monoids, Acts and Categories. De Gruyter Expositions in Mathematics, (29), https://doi.org/10.1515/9783110812909.
  • 51. Pant S, Dagtoros K, Kholil MI and Vivas A. (2024). Matrices: Peculiar determinant property. OPS Journal, 1: 1–7.

Complementary Extended Gamma Operation: A New Soft Set Operation

Yıl 2024, Cilt: 7 Sayı: 1, 15 – 44, 30.06.2024

Aslıhan Sezgin Murat Sarıalioğlu

https://doi.org/10.38061/idunas.1482044

Öz

Since its beginnings, soft set theory has shown to be a useful mathematical framework for addressing problems involving uncertainty, proving its usefulness in a variety of academic and practical disciplines. The operations of soft sets are at the very core concept of this theory. In this regard, a new kind of soft set operation known as the complementary extended gamma operation for soft sets is presented in order to improve the theory and theoretically contribute to it in this study. To shed light on the relation between the complementary extended gamma operation and other soft set operations, a thorough analysis of this operation’s attributes, including its distributions across other soft set operations, has been conducted. Additionally, this paper aims to contribute to the literature on soft sets by examining the algebraic structure of soft sets from the perspective of soft set operations, which provides a thorough grasp of their use as well as an appreciation of the ways in which soft sets can be applied to both classical and nonclassical logical thought.

Anahtar Kelimeler

Soft set, Soft Set Operations, Complementary Extended Soft Set Operations

Kaynakça

  • 1. Molodtsov D. (1999) Soft set theory-first results. Comput Math Appl. 37 (1): 19-31.
  • 2. Maji PK, Biswas R and Roy AR. (2003) Soft set theory. Comput Math Appl. 45 (1): 555-562.
  • 3. Pei D and Miao D. (2005) From soft sets to information systems. In: Proceedings of Granular Computing IEEE, 2: 617-621.
  • 4. Ali MI, Feng F, Liu X, Min WK and Shabir M. (2009) On some new operations in soft set theory. Comput Math Appl,57(9): 1547-1553.
  • 5. Sezgin A and Atagün AO. (2011) On operations of soft sets. Comput Math Appl, 61(5):1457-1467.
  • 6. Ali MI, Shabir M, Naz M. (2011) Algebraic structures of soft sets associated with new operations, Comput Math Appl, 61: 2647–2654.
  • 7. Sezgin A, Shahzad A and Mehmood A.(2019) New operation on soft sets: Extended difference of soft sets. J New Theory, (27): 33-42.
  • 8. Stojanovic NS. (2021) A new operation on soft sets: Extended symmetric difference of soft sets. Military Technical Courier, 69(4): 779-791.
  • 9. Eren ÖF and Çalışıcı H. (2019) On some operations of soft sets, The Fourth International Conference on Computational Mathematics and Engineering Sciences, Antalya.
  • 10. Sezgin A and Çalışıcı H. (2024) A comprehensive study on soft binary piecewise difference operation. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B-Teorik Bilimler, 12 (1): 32-54.
  • 11. Çağman N. (2021) Conditional complements of sets and their application to group theory. J New Results Sci. 10 (3): 67-74.
  • 12. Sezgin A, Çağman N, Atagün AO and Aybek FN. (2023a) Complemental binary operations of sets and their application to group theory. Matrix Science Mathematic, 7 (2): 114-121.
  • 13. Aybek FN. New restricted and extended soft set operations, MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 14. Sezgin A and Atagün AO. (2023) New soft set operation: Complementary soft binary piecewise plus operation. Matrix Science Mathematic, 7 (2) 125-142.
  • 15. Sezgin A and Aybek FN. (2023) New soft set operation: Complementary soft binary piecewise gamma operation. Matrix Science Mathematic (7) 1: 27-45.
  • 16. Sezgin A, Aybek FN and Güngör N.B. (2023b) New soft set operation: Complementary soft binary piecewise union operation. Acta Informatica Malaysia, 7(1): 38-53.
  • 17. Sezgin A, Aybek FN and Atagün AO. (2023c) New soft set operation: Complementary soft binary piecewise intersection operation. BSJ Eng Sci 6 (4): 330-346.
  • 18. Sezgin A and Çağman N. (2024) New soft set operation: Complementary soft binary piecewise difference operation. Osmaniye Korkut Ata Üniv Fen Biliml Derg, 7 (1): 58-94.
  • 19. Sezgin A and Demirci AM. (2023) New soft set operation: Complementary soft binary piecewise star operation. Ikonion Journal of Mathematics, 5 (2): 24-52.
  • 20. Sezgin A and Sarıalioğlu M. (2024) New soft set operation: Complementary soft binary piecewise theta operation. Journal of Kadirli Faculty of Applied Sciences, 4 (2): 325-357.
  • 21. Sezgin A and Yavuz E. (2023b) New soft set operation: Complementary Soft Binary Piecewise Lambda Operation. Sinop University Journal of Natural Sciences, 8 (2): 101-133.
  • 22. Sezgin A and Dagtoros K. (2023) Complementary soft binary piecewise symmetric difference operation: a novel soft set operation. Scientific Journal of Mehmet Akif Ersoy University, 6(2): 31-45.
  • 23. Akbulut E. New type of extended operations of soft set: Complementary extended difference and lambda operation. MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 24. Demirci AM. New type of extended operations of soft set: Complementary extended union, plus and theta operation. MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 25. Jun, Y. B. and Yang, X. (2011). A note on the paper combination of ınterval-valued fuzzy set and soft set. Comput Math Appl, 61(5): 1468-1470.
  • 26. Liu, X., Feng, F. and Jun, Y. B. (2012). A note on generalized soft equal relations. Comput Math Appl, 64(4): 572-578.
  • 27. Feng, F. and Li, Y. (2013). Soft subsets and soft product operations. Inform Sci, 44-57.
  • 28. Abbas, M., Ali, B. and Romaguera, S. (2014). on generalized soft equality and soft lattice structure. Filomat, 28(6): 1191-1203.
  • 29. Abbas, M., Ali, M.I., Romaguera, S., (2017) Generalized operations in soft set theory via relaxed conditions on parameters, Filomat 31(19): 5955–5964.
  • 30. Al-shami, T.M., (2019) Investigation and corrigendum to some results related to g-soft equality and g f -soft equality relations. Filomat, 33: 3375–3383.
  • 31. Alshasi, T., El-Shafei., T., (2020) T-soft equality relation, Turkish Journal of Mathematics, 44 (4): Article 25.
  • 32. Ali, B., Saleem, N., Sundus, N, Khaleeq, S, Saeed, M., George, R. A., (2022) Contribution to the theory of soft sets via generalized relaxed operations, Mathematics, 10: 26-36.
  • 33. Çağman N, Çitak F and Aktaş H. (2012) Soft int-group and its applications to group theory. Neural Comput Appl. 2: 151–158.
  • 34. Sezgin A and Orbay M. (2022) Analysis of semigroups with soft intersection ideals. Acta Univ Sapientiae Math. 14 (1): 166-210.
  • 35. Mahmood T, Rehman ZU and Sezgin A.(2018) Lattice ordered soft near rings. Korean J Math. 26 (3): 503-517.
  • 36. Jana C, Pal M, Karaaslan F and Sezgin A. (2019) (α, β)-soft intersectional rings and ideals with their applications. New Math Nat Comput. 15 (2): 333–350.
  • 37. Muştuoğlu E, Sezgin A and Türk ZK. (2016) Some characterizations on soft uni-groups and normal soft uni-groups. Int J Comput Appl. 155 (10): 1-8.
  • 38. Sezer AS, Çağman N and Atagün AO. (2015) Uni-soft substructures of groups. Ann Fuzzy Math Inform, 9 (2): 235–246.
  • 39. Sezer AS. (2014) Certain Characterizations of LA-semigroups by soft sets. J Intell Fuzzy Syst, 27 (2): 1035-1046.
  • 40. Özlü Ş and Sezgin A. (2020) Soft covered ideals in semigroups. Acta Univ Sapientiae Math, 12 (2): 317-346.
  • 41. Atagün AO and Sezgin A. (2018) Soft subnear-rings, soft ideals and soft n-subgroups of near-rings. Math Sci Letters, 7 (1): 37-42.
  • 42. Sezgin A. (2018) A new view on AG-groupoid theory via soft sets for uncertainty modeling. Filomat, 32 (8): 2995–3030.
  • 43. Iftikhar M and Mahmood T. (2018) Some results on lattice ordered double framed soft semirings, International Journal of Algebra and Statistics, 7: 123-140.
  • 44. Sezgin A, Çağman N and Atagün AO. (2017) A completely new view to soft intersection rings via soft uni-int product. Appl Soft Comput, 54: 366-392.
  • 45. Mahmood T, Waqas A and Rana M.A. (2015) Soft Intersectional Ideals in Ternary Semirings, Science International, 27 (5): 3929-3934.
  • 46. Sezgin A, Atagün AO and Çağman N and Demir H. (2022) On near-rings with soft union ideals and applications. New Math Nat Comput. 18 (2): 495-511.
  • 47. Yavuz E. Soft binary piecewise operations and their properties. MSc Thesis, Amasya University, Amasya, Türkiye, 2024.
  • 48. Sezgin A and Yavuz E. (2023a) A new soft set operation: Soft binary piecewise symmetric difference operation. Necmettin Erbakan University Journal of Science and Engineering, 5 (2): 189-208.
  • 49. Clifford, A. H. (1954). Bands of semigroups, Proc Am Math Soc, 5(3): 499–504.
  • 50. Kilp M., Knauer U and Mikhalev A. (2001). Monoids, Acts and Categories. De Gruyter Expositions in Mathematics, (29), https://doi.org/10.1515/9783110812909.
  • 51. Pant S, Dagtoros K, Kholil MI and Vivas A. (2024). Matrices: Peculiar determinant property. OPS Journal, 1: 1–7.

Toplam 51 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
BölümMakaleler
Yazarlar

Aslıhan Sezgin Amasya University 0000-0002-1519-7294 Türkiye

Murat Sarıalioğlu AMASYA ÜNİVERSİTESİ 0009-0009-3416-5923 Türkiye

Yayımlanma Tarihi30 Haziran 2024
Gönderilme Tarihi10 Mayıs 2024
Kabul Tarihi13 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 7 Sayı: 1

Kaynak Göster

APASezgin, A., & Sarıalioğlu, M. (2024). Complementary Extended Gamma Operation: A New Soft Set Operation. Natural and Applied Sciences Journal, 7(1), 15-44. https://doi.org/10.38061/idunas.1482044

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