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Year 2019, Volume: 2 Issue: 1, 51 - 54, 30.10.2019

Murat Kirisci , Necip Şimşek

Abstract

References

  • [1] L.A. Zadeh, Fuzzy sets, Inf. Comp., 8 (1965), 338–353.
  • [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 7–96.
  • [3] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Inter. J. Pure Appl. Math. 24 (2005), 287–297.
  • [4] I. Turksen, Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20 (1996), 191–210.
  • [5] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Inf. Comp., 31 (1989), 343–349.
  • [6] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Phoenix: Xiquan, 2003.
  • [7] R.R. Yager,Pythagorean fuzzy subsets, In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada; 2013.
  • [8] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 336–344.
  • [9] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), 215–229.
  • [10] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395–399.
  • [11] A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365–368.
  • [12] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22 (2004), 1039-1046.
  • [13] T. Bera, N.K. Mahapatra, Neutrosophic Soft Linear Spaces, Fuzzy Information and Engineering, 9 (2017), 9, 299–324.
  • [14] T. Bera, N.K. Mahapatra, Neutrosophic Soft Normed Linear Spaces, Neutrosophic Sets and Systems, 23 (2018), 52–71.
  • [15] H. Wang, F. Smarandache, Y.Q. Zhang, R. Sunderraman, Single valued neutrosophic sets Multispace and Multistructure, 4 (2010), 410–413.
  • [16] J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, J. Intell. Fuzzy Syst., 26 (2014), 2459–2466.
  • [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.

On a New Metric Space

Year 2019, Volume: 2 Issue: 1, 51 - 54, 30.10.2019

Murat Kirisci , Necip Şimşek

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] L.A. Zadeh, Fuzzy sets, Inf. Comp., 8 (1965), 338–353.
  • [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 7–96.
  • [3] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Inter. J. Pure Appl. Math. 24 (2005), 287–297.
  • [4] I. Turksen, Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, 20 (1996), 191–210.
  • [5] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Inf. Comp., 31 (1989), 343–349.
  • [6] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Phoenix: Xiquan, 2003.
  • [7] R.R. Yager,Pythagorean fuzzy subsets, In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada; 2013.
  • [8] I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 336–344.
  • [9] O. Kaleva, S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984), 215–229.
  • [10] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395–399.
  • [11] A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365–368.
  • [12] J.H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22 (2004), 1039-1046.
  • [13] T. Bera, N.K. Mahapatra, Neutrosophic Soft Linear Spaces, Fuzzy Information and Engineering, 9 (2017), 9, 299–324.
  • [14] T. Bera, N.K. Mahapatra, Neutrosophic Soft Normed Linear Spaces, Neutrosophic Sets and Systems, 23 (2018), 52–71.
  • [15] H. Wang, F. Smarandache, Y.Q. Zhang, R. Sunderraman, Single valued neutrosophic sets Multispace and Multistructure, 4 (2010), 410–413.
  • [16] J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, J. Intell. Fuzzy Syst., 26 (2014), 2459–2466.
  • [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.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Murat Kirisci 0000-0003-4938-5207

Necip Şimşek

Publication Date October 30, 2019
Acceptance Date September 18, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Kirisci, M., & Şimşek, N. (2019). On a New Metric Space. Conference Proceedings of Science and Technology, 2(1), 51-54.
AMA Kirisci M, Şimşek N. On a New Metric Space. Conference Proceedings of Science and Technology. October 2019;2(1):51-54.
Chicago Kirisci, Murat, and Necip Şimşek. “On a New Metric Space”. Conference Proceedings of Science and Technology 2, no. 1 (October 2019): 51-54.
EndNote Kirisci M, Şimşek N (October 1, 2019) On a New Metric Space. Conference Proceedings of Science and Technology 2 1 51–54.
IEEE M. Kirisci and N. Şimşek, “On a New Metric Space”, Conference Proceedings of Science and Technology, vol. 2, no. 1, pp. 51–54, 2019.
ISNAD Kirisci, Murat - Şimşek, Necip. “On a New Metric Space”. Conference Proceedings of Science and Technology 2/1 (October 2019), 51-54.
JAMA Kirisci M, Şimşek N. On a New Metric Space. Conference Proceedings of Science and Technology. 2019;2:51–54.
MLA Kirisci, Murat and Necip Şimşek. “On a New Metric Space”. Conference Proceedings of Science and Technology, vol. 2, no. 1, 2019, pp. 51-54.
Vancouver Kirisci M, Şimşek N. On a New Metric Space. Conference Proceedings of Science and Technology. 2019;2(1):51-4.
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