An approach to pre-separation axioms in neutrosophic soft topological spaces

Year 2020, Volume: 69 Issue: 2, 1389 - 1404, 31.12.2020

Ahu Açıkgöz , Ferhat Esenbel

https://doi.org/10.31801/cfsuasmas.749946

Cited By: 7

Abstract

In this study, we introduce the concept of neutrosophic soft pre-open (neutrosophic
soft pre-closed) sets and pre-separation axioms in neutrosophic soft topological spaces. In
particular, the relationship between these separation axioms are investigated. Also, we give
a new definition for neutrosophic soft topological subspace and define neutrosophic soft pre
irresolute soft and neutrosophic pre irresolute open soft functions.

Keywords

Neutrosophic pre open soft set, neutrosophic soft pre interior point, neutrosophic soft pre cluster point, neutrosophic soft pre-separation axioms, neutrosophic soft subspace

References

• Al-shami, T.M., Kocinac, Lj.D.R., The equivalence between the enriched and extended soft topologies, Appl. Comput. Math., 18 (2) (2019), 149-162.
• Aras, C.G., Sonmez, A., Çakalli, H., An approach to soft functions, J. Math. Anal., 8 2 (2017), 129-138.
• Aras, C.G., Ozturk, T.Y., Bayramov, S., Separation axioms on neutrosophic soft topological spaces, Turk. J. Math., 43 (2019), 498-510.
• Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87-96.
• Bayramov, S., Gunduz, C., On intuitionistic fuzzy soft topological spaces, TWMS J. Pure Appl. Math., 5 (2014), 66-79.
• Bayramov, S., Gunduz, C., A new approach to separability and compactness in soft topological spaces, TWMS J Pure Appl. Math., 9 (2018), 82-93.
• Bera, T., Mahapatra, N.K., On neutrosophic soft function, Annals of Fuzzy Mathematics and Informatics, 12 (1) (July 2016), 101-119.
• Bera, T., Mahapatra, N.K., Introduction to neutrosophic soft topological space, Opsearch, 54 (2017), 841-867.
• Cagman, N., Karatas, S., Enginoglu, S., Soft topology, Comput Math. Appl., 62 (2011), 351-358.
• Çakalli, H., Das, P., Fuzzy compactness via summability, Appl. Math. Lett., 22 (11) (2009), 1665-1669.
• Coskun, A.E., Aras, C.G., Cakalli, H., Sonmez, A., Soft matrices on soft multisets in an optimal decision process, AIP Conference Proceedings, 1759, 1, 020099 (2016); doi: 10.1063/1.4959713.
• Deli, I., Broumi, S., Neutrosophic soft relations and some Properties, Ann. Fuzzy Math. Inform, 9 (2015), 169-182.
• Gunduz, C., Bayramov, S., On the Tietze extension theorem in soft topological spaces, Proceedings of the Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, 43 (2017), 105-115.
• Hussain, S., On some properties of intuitionistic fuzzy soft boundary, Commun. Fac. Sci. Univ. Ank. Series A1, 69 (2) (2020), 39-50.
• Maji, P.K., Neutrosophic soft set, Ann. Fuzzy Math. Inform, 5 (2013), 157-168.
• Molodtsov, D., Soft set theory-first results, Comput Math. Appl., 37 (1999), 19-31.
• Pei, D., Miao, D., From soft sets to information systems, in: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager, B. Zhang (Eds.), Proceedings of Granular Computing, in: IEEE 2 (2005), 617-621. Salma, A.A., Alblowi, S.A., Neutrosophic set and neutrosophic topological spaces, IOSR J. Math., 3 (2012), 31-35.
• Shabir, M., Naz, M., On soft topological spaces, Comput Math. Appl., 61 (2011), 1786-1799.
• Smarandache, F., Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Int. J. Pure Appl. Math., 24 (2005), 287-297.
• Xiao, Z., Chen, L., Zhong, B., Ye, S., Recognition for soft information based on the theory of soft sets, in: J. Chen (Ed.), Proceedings of ICSSSM-05, 2 (2005), 1104-1106.