Near soft topological groups based on near soft element

Yıl 2022, Cilt: 7 Sayı: 2, 53 - 57, 30.09.2022

Hatice Taşbozan

Öz

In this article, we introduce the concept of the near soft element and define the near soft group using near soft element with binary operation in the whole set non-empty near soft elements of a dedicated near soft set. The topology of this notion and continuity notions are dened in this topology. The concept of near soft topological group was created with the help of continuous transformations defined on the near soft group. These new concepts were given with examples.

Anahtar Kelimeler

Near set, Soft Set, Near Soft Set, Near Soft Element, Near Soft Group, Near Soft Topological Group .

Kaynakça

• [1]J.F.Peters, Near sets: Special Theory about nearness of objects, Fund. Informaticae. 75(2007) 407-433.
• [2] J.F.Peters, Near sets: General Theory about nearness of objects, App.Math. Sci. 1(2007) 2609-2629.
• [3] P.K.Maji, R.Biswas, A.R.Roy, Soft set theory, Comput. Math. appl. 45(2003) 555-562.
• [4] D.Molodtsov, Soft set theory-rst results, Comput. Math.appl. 37(1999) 19-31.
• [5] F.Feng, C.Li, B.Davvaz, M.I.Ali, Soft sets combined with fuzzy sets and rough sets, Soft comput. 14 (2010) 899-911.
• [6] N.Cagman, S.Karatas, S.Enginouglu, M.I.Ali, Soft Topology, Computers and Mathematics with Applications 62 (2011) 351-358.
• [7] H.Aktas,N.Cagman, Soft sets and soft groups, Inform. Sci. 177(2007) 2726- 2735.
• [8] D. Wardowski, On a soft mapping and its xed points, Fixed point theory and Applications 182, (2013)1-11.
• [9] J. Ghosh, D.Mandal, T.K.Samanta, Soft group based on soft element, Jordan journal of mathematics and Statistics 9(2), (2016) 141-159.
• [10] J. Ghosh, T.K. Samanta, Soft set functions and soft set groups, Pure and Applied Mathematics Letters, (2016) 8-14.
• [11] H. Tasbozan, I.Icen, N.Bagirmaz, A.F. Ozcan, Soft sets and soft topology on nearness approximation spaces, Filomat, 13 (2017) 4117-4125.
• [12] H. Tasbozan, Near soft groupoid, Ikonion Journal of Mathematics,(2020) 2(2), 35-39.
• [13] H. Tasbozan, Near Approximations in Vector Spaces, Journal of Universal Mathematics, (2020) 3(2), 114-120.
• [14] H. Tasbozan, Near Soft Connectedness, Afyon Kocatepe University Journal of Science and Engineering,(2020) 20(5), 815-818.
• [15] N.Bagirmaz, H. Tasbozan, The left right rough approximations in a group, JP Journal of Algebra, Number Theory and Applications,(2019) 42(1), 77- 83.
• [16] H. Tasbozan, I.Icen, The Upper and Lower Approximations in Rough Sub- groupoid of a Groupoid, Moroccan Journal of Pure and Applied Analysis, (2018) 4(2), 85-93.
• [17] C.N. Polat, G. Yaylali, B. Tanay, A new approach for soft semi-topological groups based on soft element, Filomat,(2018) 32(16), 5743-5751.
• [18] S.H. Hamzah, M.Q. Atshan, Separation Axioms on Soft Topological Groups, AL-Qadisiyah Journal of Pure Science,(2018) 23(3), 47-60.