ON SOFT RING AND SOFT TOPOLOGICAL RING

Yıl 2023, , 148 - 157, 28.08.2023

Nazan Polat , Gözde Yaylalı Umul , Bekir Tanay

https://doi.org/10.20290/estubtdb.1231907

Cited By: 1

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.

Anahtar Kelimeler

Soft set, Soft ring, Soft topological ring

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