Araştırma Makalesi
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ON SOFT RING AND SOFT TOPOLOGICAL RING

Yıl 2023, , 148 - 157, 28.08.2023
https://doi.org/10.20290/estubtdb.1231907

Öz

Soft set theory is an affective mathematical tool to solve problems that involves uncertainties. Despite the development in the theoretical structure of soft sets, researchers did not make consensus formulation of soft element. In this study soft ring is redefined by the help of soft operation which are based on a natural definition of soft element. This new soft ring definition is compared with the soft ring definition in the literature. Some examples, results and theorems are given to enrich the concept of soft ring. Also soft topological ring structure which is a harmonization of soft ring and soft topology is studied with some results.

Kaynakça

  • [1] Molodtsov D. Soft set theory-first result. Comput Math Appl 1999; 37: 19-31.
  • [2] Maji PK, Biswas R, Roy AR. Soft set theory. Comput Math Appl 2003; 45: 555-562.
  • [3] Çağman N, Karataş S, Enginoglu S. Soft topology. Comput. Math Appl 2011; 62(1): 351-358.
  • [4] Shabir M, Naz M. On soft topological spaces. Comput. Math Appl 2011; 61(7): 1786-1799.
  • [5] Roy S, Samanta TK. An introduction of a soft topological spaces. Proceeding of UGC sponsored national seminar on recent trends in fuzzy set theory, Rough set theory and Soft set theory at Uluberia College on 23rd and 24th September, 2011 ISBN 978-81-922305-5-9, 9-12, 2011.
  • [6] Roy S, Samanta TK. A note on a soft topological space. Journal of Mathematics 2014; 46(1): 19-24.
  • [7] Cagman N, Enginoglu S. Soft set theory and uni-int decision making. Eur J Oper Res 2010; 207: 848-855.
  • [8] Aktaş H, Çağman N. Soft sets and soft groups. Inf Sci 2007; 177: 2726-2735.
  • [9] Acar U, Koyuncu F, Tanay B. Soft sets and soft rings. Comput Math Appl 2010; 59: 3458-3463.
  • [10] Ghosh J, Mandal D, Samanta TK. Soft groups based on soft element. Jordan J Math Stat 2016; 9 (2): 141-159.
  • [11] Sun QM, Zhang ZL, Liu J. Soft sets and soft modules. Lecture Notes in Computer Science 2008; 5009: 403–409.
  • [12] Gunduz (Aras) C, Bayramov S, Fuzzy Soft Modules. International Mathematical Forum 2011; 6(11): 517 – 527
  • [13] Wardowski D. On a soft mapping and its fixed points. J Fixed Point Theory Appl 2013; 182: 1-11.
  • [14] Polat NÇ, Yaylalı G, Tanay B. A new approach for soft semi-topological groups based on soft element. Filomat, 2018; 32(16): 5743-5751.
  • [15] Polat NÇ, Yaylalı G, Tanay B. Some results on soft element and soft topological space. Math. Methods Appl Sci 2018; 42(16): 5607-5614.
  • [16] Tanay B, (Polat) Çakmak N. Soft Semi-Topological Groups. J Interdisc Math 2014; 17 (4): 355-363.
  • [17] Shah T, Shaheen S. Soft Topological Groups and Rings. Ann Fuzzy Math Inform 2013; 7 (5): 725-743.
  • [18] Tahat MK, Sidky F, Abo-Elhamayel A. Soft topological soft groups and soft rings. Soft computing 2018; 22: 7143-7156.
  • [19] Tahat MK, Sidky F, Abo-Elhamayel A. Soft topological rings. Journal of King Saud University 2019; 31(4): 1127-1136.
  • [20] Hida T. Soft topological group. Ann Fuzzy Math Inform 2014; 8: 1001-1025
  • [21] Nazmul S, Samanta SK. Soft topological groups. Kochi J Math 2010; 5: 151-161

ON SOFT RING AND SOFT TOPOLOGICAL RING

Yıl 2023, , 148 - 157, 28.08.2023
https://doi.org/10.20290/estubtdb.1231907

Öz

Soft set theory is an affective mathematical tool to solve problems that involves uncertainties. Despite the development in the theoretical structure of soft sets, researchers did not make consensus formulation of soft element. In this study soft ring is redefined by the help of soft operation which are based on a natural definition of soft element. This new soft ring definition is compared with the soft ring definition in the literature. Some examples, results and theorems are given to enrich the concept of soft ring. Also soft topological ring structure which is a harmonization of soft ring and soft topology is studied with some results.

Kaynakça

  • [1] Molodtsov D. Soft set theory-first result. Comput Math Appl 1999; 37: 19-31.
  • [2] Maji PK, Biswas R, Roy AR. Soft set theory. Comput Math Appl 2003; 45: 555-562.
  • [3] Çağman N, Karataş S, Enginoglu S. Soft topology. Comput. Math Appl 2011; 62(1): 351-358.
  • [4] Shabir M, Naz M. On soft topological spaces. Comput. Math Appl 2011; 61(7): 1786-1799.
  • [5] Roy S, Samanta TK. An introduction of a soft topological spaces. Proceeding of UGC sponsored national seminar on recent trends in fuzzy set theory, Rough set theory and Soft set theory at Uluberia College on 23rd and 24th September, 2011 ISBN 978-81-922305-5-9, 9-12, 2011.
  • [6] Roy S, Samanta TK. A note on a soft topological space. Journal of Mathematics 2014; 46(1): 19-24.
  • [7] Cagman N, Enginoglu S. Soft set theory and uni-int decision making. Eur J Oper Res 2010; 207: 848-855.
  • [8] Aktaş H, Çağman N. Soft sets and soft groups. Inf Sci 2007; 177: 2726-2735.
  • [9] Acar U, Koyuncu F, Tanay B. Soft sets and soft rings. Comput Math Appl 2010; 59: 3458-3463.
  • [10] Ghosh J, Mandal D, Samanta TK. Soft groups based on soft element. Jordan J Math Stat 2016; 9 (2): 141-159.
  • [11] Sun QM, Zhang ZL, Liu J. Soft sets and soft modules. Lecture Notes in Computer Science 2008; 5009: 403–409.
  • [12] Gunduz (Aras) C, Bayramov S, Fuzzy Soft Modules. International Mathematical Forum 2011; 6(11): 517 – 527
  • [13] Wardowski D. On a soft mapping and its fixed points. J Fixed Point Theory Appl 2013; 182: 1-11.
  • [14] Polat NÇ, Yaylalı G, Tanay B. A new approach for soft semi-topological groups based on soft element. Filomat, 2018; 32(16): 5743-5751.
  • [15] Polat NÇ, Yaylalı G, Tanay B. Some results on soft element and soft topological space. Math. Methods Appl Sci 2018; 42(16): 5607-5614.
  • [16] Tanay B, (Polat) Çakmak N. Soft Semi-Topological Groups. J Interdisc Math 2014; 17 (4): 355-363.
  • [17] Shah T, Shaheen S. Soft Topological Groups and Rings. Ann Fuzzy Math Inform 2013; 7 (5): 725-743.
  • [18] Tahat MK, Sidky F, Abo-Elhamayel A. Soft topological soft groups and soft rings. Soft computing 2018; 22: 7143-7156.
  • [19] Tahat MK, Sidky F, Abo-Elhamayel A. Soft topological rings. Journal of King Saud University 2019; 31(4): 1127-1136.
  • [20] Hida T. Soft topological group. Ann Fuzzy Math Inform 2014; 8: 1001-1025
  • [21] Nazmul S, Samanta SK. Soft topological groups. Kochi J Math 2010; 5: 151-161
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Topoloji
Bölüm Makaleler
Yazarlar

Nazan Polat 0000-0002-6893-9124

Gözde Yaylalı Umul 0000-0001-8191-2674

Bekir Tanay 0000-0003-4066-2044

Yayımlanma Tarihi 28 Ağustos 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Polat, N., Yaylalı Umul, G., & Tanay, B. (2023). ON SOFT RING AND SOFT TOPOLOGICAL RING. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 11(2), 148-157. https://doi.org/10.20290/estubtdb.1231907
AMA Polat N, Yaylalı Umul G, Tanay B. ON SOFT RING AND SOFT TOPOLOGICAL RING. Estuscience - Theory. Ağustos 2023;11(2):148-157. doi:10.20290/estubtdb.1231907
Chicago Polat, Nazan, Gözde Yaylalı Umul, ve Bekir Tanay. “ON SOFT RING AND SOFT TOPOLOGICAL RING”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 11, sy. 2 (Ağustos 2023): 148-57. https://doi.org/10.20290/estubtdb.1231907.
EndNote Polat N, Yaylalı Umul G, Tanay B (01 Ağustos 2023) ON SOFT RING AND SOFT TOPOLOGICAL RING. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 11 2 148–157.
IEEE N. Polat, G. Yaylalı Umul, ve B. Tanay, “ON SOFT RING AND SOFT TOPOLOGICAL RING”, Estuscience - Theory, c. 11, sy. 2, ss. 148–157, 2023, doi: 10.20290/estubtdb.1231907.
ISNAD Polat, Nazan vd. “ON SOFT RING AND SOFT TOPOLOGICAL RING”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 11/2 (Ağustos 2023), 148-157. https://doi.org/10.20290/estubtdb.1231907.
JAMA Polat N, Yaylalı Umul G, Tanay B. ON SOFT RING AND SOFT TOPOLOGICAL RING. Estuscience - Theory. 2023;11:148–157.
MLA Polat, Nazan vd. “ON SOFT RING AND SOFT TOPOLOGICAL RING”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, c. 11, sy. 2, 2023, ss. 148-57, doi:10.20290/estubtdb.1231907.
Vancouver Polat N, Yaylalı Umul G, Tanay B. ON SOFT RING AND SOFT TOPOLOGICAL RING. Estuscience - Theory. 2023;11(2):148-57.

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