SEPARATION AXIOMS ON NEAR SOFT TOPOLOGICAL SPACES

Abstract

Near soft sets are a very successful mathematical model that has been used in order to express the decision-making process for uncertainty in a more ideal way, especially in recent years. The purpose of this paper is to contribute to the theoretical studies on near soft topological spaces. In addition, it presents basic concepts and constructs that will form the basis for a near theoretical set-up of near soft topological spaces. These concepts and structures include sub near soft set, near soft subspaces of a near soft topological space and near soft $T_i$-spaces for $0\leq i\leq 4$. The important aspects of the paper are discussed, especially by examining the definitions and properties given.

Keywords

• Near soft set
• Near soft topological space
• Near soft separation axioms

References

1. L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338-353.
2. D. Molodtsov, Soft set theory first results, Comput. Math. Appl., 37 (1999) 19-31.
3. H. Tasbozan, I. Icen, N. Bagirmaz, A.F. Ozcan, Soft sets and soft topology on nearness approximation spaces, Filomat, 31(13) (2017) 4117-4125.
4. A. Özkan, On near soft sets, Turkish Journal of Mathematics, 43 (2019) 1005–1017.
5. J.F. Peters, Near sets. Special theory about nearness of objects, Fundementa Informaticae, 75 (2007) 407-433.
6. J.F. Peters JF. Near sets. General theory about nearness of objects, Applied Mathematical Sciences, 1 (2007) 2609-2629.
7. M.A. Ozturk, E. Inan, Soft nearness approximation spaces, Fund. Inform., 124 (2013) 231–250.
8. Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11(5) (1982) 341–356.

9. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87–96.
10. K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64 (1994) 159–174.
11. F. Feng, C. Li, B. Davvaz and I.M. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing, 14(9) (2010) 899–911.
12. F. Feng, X. Liu, F.L. Violeta and J.B. Young, Soft sets and soft rough sets, Inform. Sci., 181 (2011) 1125–1137.
13. D. Chen, E.E.C. Tsong, D.S. Young and X. Wong, The parametrization reduction of soft sets and its applications, Comput. Math. Appl., 49 (2005) 757–763.
14. F. Feng, Y.B. Jun, X. Liu and L.F. Li, An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math., 234 (2010) 10–20.
15. Y. Jiang, Y. Tang, Q. Chen, J.Wang and S. Tang, Extending soft sets with description logics, Comput. Math. Appl., 59 (2010) 2087–2096.
16. Y.B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56(5) (2008) 1408–1413 .
17. Y.B. Jun and C.H. Park, Applications of soft sets in ideal theory of BCK/BCIalgebras, Inform. Sci., 178(11) (2008) 2466–2475.
18. P.K. Maji, A.R. Roy and R. Biswas, An application of soft sets in desicion making problem, Comput. Math. Appl., 44 (2002) 1077–1083.
19. D. Pei and D. Miao, From soft sets to information systems, in Proceedings of the IEEE International Conference on Granular Computing, 2 (2005) 617–621.