Some notes on soft neighborhood

Document Type : Research Paper

Authors

1 Department of Mathematics, Mugla Stk Kocman University, 48170 Mugla, Turkey

2 Department of Mathematics, Mugla Stk Kocman University, 48170 Mugla, Turkey

Abstract

In this paper, the concept of soft neighborhood of an element in a soft topological space is introduced, and its basic
prop-erties are studied.

Keywords


[1] U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl.,59 (11) (2010) 3458-3463.
[2] H. Akta¸s, N. C¸ a˘gman, Soft sets and soft groups, Inform. Sci., 177 (13) (2007)2726-2735.
[3] M.I. Ali, F. Feng, X. Liu, W.K. Min, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009) 1547-1553.
[4] A.A. Allam, T.H. Ismail, R. Mohammed, A new approach to soft belonging, Ann.Fuzzy Math. Inform., 13 (1)(2017)
145-152.
[5] A. Ayg¨uo˘glu, H. Ayg¨un, Some notes on soft topological spaces, Neural Comput.& Applic., 21 (1) (2012) 113-119.
[6] N. C¸ a˘gman, S. Engino˘glu,Soft set theory and uni−int decision making,EuropeanJ.Oper.Res.,207(2)(2010) 848-855.
[7] V. C¸ etkin, A. Ayg¨uo˘glu, H. Ayg¨un, A new approach in handling soft decision making problems, J. Nonlinear Sci. Appl., 9 (2016) 231-239.
[8] S. Das, S.K. Samanta, Soft real sets ,soft real numbers and their properties, Jour-nal of Fuzzy Mathematics, 20 (3)
(2012) 551-576.
[9] S. Das, S.K. Samanta, On soft metric spaces, Journal of Fuzzy Mathematics, 21(3) (2013) 1-28.
[10] N. Ghosh, D. Mandal, T. Samantha, Soft groups based on soft element, Jordan J Math Stat., 9(2) (2016) 141-159.
[11] S. Hussain, B. Ahmad, Some properties of soft topological spaces, Comput. Math.Appl., 62 (11) (2011) 4058-4067.
[12] M.B. Kandemir, A new perspective on soft topology, Hittite J. Sci. Eng., 5 (2) (2018) pp.105–113.
[13] M.B. Kandemir, Some notes on soft topological concepts and an application method, Mathematical Sciences and Applications E-Notes, 8 (1) (2020) 105–116
[14] M.B. Kandemir, Monotonic soft sets and its applications, Annals of Fuzzy Mathematics and Informatics, 12 (2) (2016) 295-307.
[15] M.B. Kandemir, The concept of σ-algebraic soft set, Soft Comp., 22 (13) (2018) 4353-4360.
[16] M.B. Kandemir, Some notes on σ-algebraic soft sets, Annals of the University of Craiova - Mathematics and Computer Science Series, 47 (2) (2020) 387-396.
[17] P.K. Maji, R. Biswas, A.R. Roy, Soft set theory. Comput. Math. Appl., 45 (2003) 555-562.
[18] P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (8-9) (2002) 1077-1083.
[19] D. Molodtsov, Soft set theory - first results. Comput. Math. Appl., 37 (1999),19-31.
[20] S.K. Nazmul, S.K. Samanta, Neighbourhood properties of soft topological spaces, Ann. Fuzzy Math. Inform.,
6 (1) (2013) 1-15.
[21] N. C¸ akmak Polat, G. Yaylalı, B. Tanay, Some results on soft element and soft topological space, Math. Meth. Appl. Sci., (2019) 5607-5614.
[22] K. Qin, J. Yang, X. Zhang, Soft set approaches to decision making problems, In.T. Li et al. (eds) Rough Sets and Knowledge Technology RSTK 2012. Lecture Notes in Computer Science, 7414 (2012), 456-464.
[23] M. Saeed, M. Hussain, A.A. Mughal, A studuy of soft sets with soft members and soft elements: A new approach, Punjab University Journal of Mathematics, 52(8) (2020) 1-15.
[24] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (7)(2011) 1786-1799.