Volume 3 , Issue 2 , PP: 19-31, 2022 | Cite this article as | XML | Html | PDF
G.Gincy 1 * , Dr.C.Janaki 2 , W.F.Al Omeri 3
Doi: https://doi.org/10.54216/JNFS.030202
In this article, Bipolar neutrosophic nano topology is introduced and some of its properties are studied. We found that, it is difficult to find a nano topology for every bipolar neutrosophic set. So we introduced a bipolar neutrosophic nano topology, which is a generalization of bipolar neutrosophic nano topology and its fundamental features are investigated with appropriate examples. This approach is used for real life multi criteria decision making situations. The practical problems may be solved by finding CORE values through the criterion reduction.One can apply the basis of the bipolar neutrosophic nano topology as the key factors of a particular decision making problem using topological reduction of attributes in complete or incomplete information system.
Nano topology , Bipolar set, Fuzzy set , Neutrosophic set , Intuitionistic fuzzy set , Neutrosophic nano topology , Bipolar Neutrosophic set , Bipolar Neutrosophic nano topology , Bipolar Neutrosophic nano , , topology.
[1] Akram M., Ishfaq N., Smarandache F., Broumi S., Application of Bipolar Neutrosophic sets to Incidence
Graphs, Neutrosophic Sets and Systems, 2019, 27, 180-200.
[2] Ali M., Son L. H., Deli I., N.D. Tien, Bipolar neutrosophic soft sets and applications in decision making,
Journal of Intelligent & Fuzzy Systems, 2017, 33, 4077-4087.
[3] Arokiarani I., Dhavaseelan R., Jafari S. and Parimala M., On some new notions and functions in
neutrosophic topological spaces, Neutrosophic Sets and Systems, 2017, 16, 16-19.
[4] Atanassov K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 1986, 20(1), 87-96.
[5] Atanassov K., Review and new results on Intuitionistic fuzzy sets, Preprint IM-MFAIS, Sofia, 1988, 1-88.
[6] Atanassov K. and Stoeva S., Intuitionistic fuzzy sets, in: Polish Syrup. on Interval & Fuzzy Mathematics,
Poznan, Aug 1983, 23-26.
[7] Biswas R., On fuzzy sets and intuitionistic fuzzy sets, NIFS, 1997, 3, 3-11.
[8] Bosc P., Pivert O., On a fuzzy bipolar relational algebra, Information Sciences, 2013, 219, 1-16.
[9] C.L.Chang, Fuzzy Topological spaces, J.Math. Anal. Appl., 1968, 24, 182-190.
[10] Coker D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88, 1997,
No.1,81-89.
[11] Ezhilmaran D., Sankar K., Morphism of bipolar intuitionistic fuzzy graphs. Journal of Discrete
Mathematical Sciences and Cryptography, 2015, 18(5), 605–621.
[12] Irfan Deli, Mumtaz Ali and Florentin Smarandache, Bipolar Neutrosophic Sets and Their Application
Based on Multi-Criteria Decision Making Problems, Proceedings of the 2015 International Conference on
Advanced Mechatronic Systems, Beijing, China, Aug 2015 , 22-24.
[13] Jianming Zhan, Muhammad Akram, Muzzamal Sitara, Novel decision-making method based on bipolar
neutrosophic information, Methodologies and Application, 2018, 9955-9977.
[14] Lee K. M., Comparison of interval-valued fizzy sets, intuitionistic fuzzy sets and bipolar-valued fuzzy sets,
J. Fuzzy Logic Intelligent, 2004, 14(2), 125-129.
[15] Lee K. M., Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies,
Bangkok, Thailand, 2000, 307-312.
[16] Lee S. J., Lee E. P., Intuitionistic fuzzy proximity spaces, Int. J. Math. Sci, 2004, 49, 2617-2628.
[17] Lellis Thivagar M., Saeid Jafari ,Sutha Devi V., Antonysamy V., A novel approach to nano topology via
neutrosophic sets, NSS, 2018, 20, 86-94.
[18] Lellis Thivagar M., Sutha Devi V., New sort of operators in nano ideal topology, Ultra Scientist, 2016, .28
(1)A, 51-64.
[19] Lellis Thivagar M., Carmel Richard., On nano forms of weakly open sets, International Journal of
Mathematics and Statistics Invention, 2013, 1 (1), 31-37.
[20] Lupianez F. G., On Neutrosophic sets and topology, Procedia, Computer Science, 2017, 120, 975-982.
[21] Pawlak Z., Rough set Theory, Int. J. Comput. Inf. Sci., 1982, 11 (5).
[22] Salama A. A., Albowli S. A., Neutrosophic Set and Neutrosophic Topological Spaces, IOSR Journal of
Mathematics, Sep-Oct 2012, 3(4), 31-35.
[23] Salama A. A., Smarandache F., Valeri Kroumov, Neutrosophic crisp sets via neutrosophic crisp
topological spaces. Neutrosophic Sets Syst. 2016, 13, 96–104.
[24] Smarandache F., An introduction to neutrosophic bipolar vague topological spaces, NSS, 2019, 29, 62-70.
[25] Smarandache F., A Unifying Field in Logics: Neutrosophy, Neutrosophic Set, Neutrosophic probability.
USA: Set and Logic. American Research Press, Rehoboth, NM, 1998.
[26] Smarandache F., Neutrosophic set – a generation of the intuitionistic fuzzy set, International journal of
Pure and Applied Mathematics, 2005, 24(3), 287-297.
[27] Smarandache F., Neutrosophy and Neutrosophic Logic, First international conference on Neutrosophy,
Neutrosophic logic, Set, Probability, and Statistics, University of New Maxico, Gallup, NM 87301, USA,
2002.
[28] Surapati Pramanik, Kalyan Mondal, Rough bipolar neutrosophic set, Global Journal of Engineering
Science and Research Management, June 2016, 3(6), 71-81.
[29] Taha Yasin Ozturk, Tugba Han Dizman, A New Approach to Operations on Bipolar Neutrosophic Soft Sets
and Bipolar Neutrosophic Soft Topological Spaces, NSS, 2019, 30, 22-33.
[30] Wadei Faris Al Omeri, Saeid Jafari, On Generalized Closed Sets and Generalized Pre-Closed Sets in
Neutrosophic Topological Spaces, Mathematics, 2019, 1(7), 1-12. doi:doi.org/10.3390/math7010001.
[31] Wadei Al Omeri, Smarandache F., New Neutrosophic sets via Neutrosophic topological spaces,
Neutrosophic Operational Research, 2017,1 , 189-209.
[32] Wadei Faris Al Omeri, On Mixed b-Fuzzy Topological Spaces, International Journal of Fuzzy Logic and
Intelligent Systems 2020; 20(3), 242-246, https://doi.org/10.5391/IJFI
[33] Wang H., Smarandache F., Zhang Y. et. al., Single valued neutrosophic sets, Multi space Multi struct.
Neutr. Trans., 2010, 4, 410-413.
[34] Zadeh L. A., Fuzzy sets, Information and Control, 1965, 8(3), 338-353.
