Volume 15 • Issue 2 • PP: 77-88 • 2021
Neutrosophic Soft Tri-Topological Spaces
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In this study, the concept of neutrosophic soft tri-topological space is defined as a generalization of neutrosophic soft bitopological space. Then neutrosophic soft tri-open and tri-closed sets are defined and in this space. Also, some basic properties of these new types of open and closed sets are investigated and supported by many examples to further clarify the study.
Keywords
References
[1] K.Atanassov, "Intuitionistic Fuzzy Sets", Fuzzy Sets and Systems, 20 , pp. 87-96, 1986.
[2] A. B. AL-Nafee, "New family of neutrosophic soft sets", Neutrosophic Sets and Systems., 38, pp. 482 - 496, 2020.
[3] 3.Y. Taha, G. A. Cigdem and B. Sadi, “A New Approach to Operations on Neutrosophic Soft Sets and to Neutrosophic Soft Topological Spaces", Communications in Mathematics and Applications, vol. 10(3), pp. 481 – 493, 2019.
[4] T. Bera and N.Mahapatra, "Introduction to neutrosophic soft topological space", Opsearch, 54(4), pp. 841- 867, 2017.
[5] N. Cagman, S. Karatas and S. Enginoglu, "Soft topology", Communications in Mathematics and Applications, 62, pp. 351–358, 2011.
[6] C. L. Chang "Fuzzy topological spaces" J. Math. Anal. Appl, 24(1), pp. 182–190, 1968.
[7] D. Coker “A note on intuitionistic sets and intuitionistic points", Turkish J. Math, 20, pp. 343-351, 1996.
[8] I. Deli and S. Broumi "Neutrosophic soft relations and some properties", Annals of Fuzzy Mathematics and Informatics. 9(1), pp. 169–182, 2015.
[9] H. Dadas and S. Demiralp " Introduction to neutrosophic soft bitopological spaces”, International Journal of Neutrosophic Science, 14(2), pp. 72–81, 2021.
[10]B. M. Ittanagi, “Soft bitopological spaces“, International Journal of Computer Applications, 107(7), pp. 1-4, 2014.
[11]A. B. AL-Nafee, R. Al-Hamido and F. Smarandache, “Separation axioms in neutrosophic crisp topological spaces”, Neutrosophic Sets and Systems., 25, pp. 25 - 33, 2019.
[12]R. Al-Hamido, "Neutrosophic crisp bitopological spaces", Neutrosophic Sets and Systems, vol. 21 ,pp. 66-73. 2018. https://doi.org/10.5281/zenodo.1408695
[13]A. Saha and S. Broumi, "New operators on interval valued neutrosophic sets", Neutrosophic Sets and Systems., 28, pp. 128-137, 2019. DOI: 10.5281/zenodo.3382525
[14]A. A. Salma and S.A. Alblowi, "Neutrosophic set and neutrosophic topological spaces", IOSR J. Math., 3(4), pp. 31–35. 2012.
[15]F. Smarandache, "Neutrosophic set, a generalisation of the intuitionistic fuzzy sets", Int. J. Pure Appl. Math., 24, pp. 287–297, 2005.
[16]D. N. Georgiou, A. C. Megaritis and V. I. Petropoulos, “On soft topological spaces“, Appl. Math. Inf. Sci, 7(2), pp. 1889-1901, 2013.
[17]L. Zadeh, "Fuzzy sets", Inform and Control, 8, pp. 338–353, 1965.
[18]Y. Taha, G. A. Cigdem and B. Sadi, “A New Approach to Operations on Neutrosophic Soft Sets and to Neutrosophic Soft Topological Spaces", Communications in Mathematics and Applications, vol. 10(3) , pp. 481 – 493, 2019.
[19]Y. O. Taha, G. A. Cigdem and B. Sadi, "Separation axioms on neutrosophic soft topological spaces", Turk. J. Math, 43, pp. 498-510, 2019.
[20]A. Kandil, A. A. Nouh and S. A El-Sheikh, “On fuzzy bitopological spaces “, Fuzzy sets and systems, 74(3), 353-363, 1995.
[21]J. C. Kelly,“Bitopological spaces“, Proceedings of the London Mathematical Society, 3(1), 71-89, 1963.
[22]P. Maji, "Neutrosophic soft set", Annals of Fuzzy Mathematics and Informatics, 5(1), pp.157-168, 2013.
[23]K, Mohana, V. Christy and F. Smarandache, "Multi-criteria decision-making problem via bipolar single-valued neutrosophic settings", Neutrosophic Sets and Systems., 25, pp.125-135, 2018. DOI: 10.5281/zenodo.2631512.
[24]D. Molodtsov, "Soft set theory-First results", Computers & Mathematics with Applications, 37, pp.19–31, 1999.
[25]N. A. Nabeeh, M. Abdel-Basset, H. A. El-Ghareeb and A. Aboelfetouh, "Neutrosophic multicriteria decision making approach for iot-based enterprises", IEEE Access, 7, pp. 59559-59574, 2019.
[26]N. A. Nabeeh, F. Smarandache, M. Abdel-Basset, H. A. El-Ghareeb and A. Aboelfetouh, "An integrated neutrosophic-topsis approach and its application to personnel selection: A new trend in brain processing and analysis", IEEE Access, 7, pp. 29734-29744, 2019.
[27]Y. O. Taha and O. Alkan, “Neutrosophic bitopological spaces“, Neutrosophic Sets and Systems., 30, pp. 88-97, 2019.
[28]S. Bayramov and C. Gunduz Aras, "On intuitionistic fuzzy soft topological spaces", TWMS Pure Appl. Math: 5(1), pp. 66–79, 2014.
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