On a New Metric Space

Abstract

In this presentation, the definition of new metric space with neutrosophic numbers is given. Several topological and structural properties have been investigated. The analogue of Baire Category Theorem is given for Neutrosophic metric spaces.

Keywords

• Baire Category Theorem,completeness,Hausdorffness,neutrosophic metric space

References

1. [1] L.A. Zadeh, Fuzzy sets, Inf. Comp., 8 (1965), 338–353.
2. [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 7–96.
3. [3] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Inter. J. Pure Appl. Math. 24 (2005), 287–297.
4. [4] I. Turksen, Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20 (1996), 191–210.
5. [5] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Inf. Comp., 31 (1989), 343–349.
6. [6] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Phoenix: Xiquan, 2003.
7. [7] R.R. Yager,Pythagorean fuzzy subsets, In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada; 2013.
8. [8] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 336–344.

9. [9] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), 215–229.
10. [10] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395–399.
11. [11] A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365–368.
12. [12] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22 (2004), 1039-1046.
13. [13] T. Bera, N.K. Mahapatra, Neutrosophic Soft Linear Spaces, Fuzzy Information and Engineering, 9 (2017), 9, 299–324.
14. [14] T. Bera, N.K. Mahapatra, Neutrosophic Soft Normed Linear Spaces, Neutrosophic Sets and Systems, 23 (2018), 52–71.
15. [15] H. Wang, F. Smarandache, Y.Q. Zhang, R. Sunderraman, Single valued neutrosophic sets Multispace and Multistructure, 4 (2010), 410–413.
16. [16] J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, J. Intell. Fuzzy Syst., 26 (2014), 2459–2466.
17. [17] J.J Peng, J.Q.Wang, j.Wang, H.Y. Zhang, X.H. Chen, Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems, International Journal of Systems Science, 47 (2016), 2342-2358, DOI: 10.1080/00207721.2014.994050.