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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 18Issue 4PP: 204-222 • 2022

More on Neutrosophic Nano Open Sets

A. Vadivel 1* ,
C. John Sundar 2 ,
K. Kirubadevi 3 ,
S. Tamilselvan 4
1PG and Research Department of Mathematics, Government Arts College (Autonomous), Karur - 639 005, India;Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India.
2Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India.
3Department of Mathematics, Thiruvalluvar Government Arts College, Rasipuram, Namakkal - 637 401, India.
4Mathematics Section (FEAT), Annamalai University, Annamalai Nagar - 608 002, India.
* Corresponding Author.
Received: March 18, 2022 Accepted: June 28, 2022

Abstract

In this paper, we introduce the concepts of neutrosophic nano δ-open sets and some stronger and weaker forms

of neutrosophic nano open sets in neutrosophic nano topological spaces. And, show that the set of all neutrosophic

nano δ-open sets are also a neutrosophic nano topology, which is called the neutrosophic nano δ

topology. Further, we dealt with the concepts of neutrosphic nano δ-interior and neutrosophic nano δ-closure

operators. Moreover, we define the product related neutrosophic nano topological spaces and proved some

theorems related to this.

Keywords

neutrosophic nano open neutrosophic nano &delta -open neutrosophic nano &delta -&alpha open neutrosophic nano &delta -S open neutrosophic nano &delta -P open neutrosophic nano &delta -&gamma open and neutrosophic nano &delta -&beta open AMS (2000) subject classification: 03E72 54A05 54A40.

References

[1] Al-Hamido, R.K. On neutrosophic crisp supra bi-topological spaces. International Journal of Neutrosophic

Sciences 2020, Vol 4 (1), pp 36-46.

[2] Atanassov, K.; Stoeva, S. Intuitionistic fuzzy sets. In Proceedings of the Polish Symposium on Interval

and Fuzzy Mathematics 1983, Poznan, Poland, pp 23-26.

[3] Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 1986, Vol 20, pp 87-96.

[4] Chang, C.L. Fuzzy topological spaces. J. Math. Anal. Appl. 1968, Vol 24, pp 182-190.

[5] Coker, D. An introduction to intuitionistic fuzzy topological spaces. Fuzzy sets and systems 1997, Vol

88, pp 81-89.

[6] Das, S.K.; Edalatpanah, S.A. A new ranking function of triangular neutrosophic number and its application

in inter programming. International Journal of Neutrosophic Sciences 2020, Vol 4 (2), pp 82-92.

[7] Lellis Thivagar, M.; Richard, C. On nano forms of weekly open sets. International journal of mathematics

and statistics invention 2013, Vol 1 (1), pp 31-37.

[8] Lellis Thivagar, M.; Jafari, S.; Sutha Devi, V.; Antonysamy, V. A novel approach to nano topology via

neutrosophic sets. Neutrosophic Sets and Systems 2018, Vol 20, pp 86-94.

[9] Mullai, M.; Sangeetha, K.; Surya, R.; Madhan Kumar, G.; Jayabalan, R.; Broumi, S. A single valued

neutrosophic inventory model with neutrosophic random variable. International Journal of Neutrosophic

Sciences 2020, Vol 1 (2), pp 52-63.

[10] Pankajam, V.; Kavitha, K. δ-open sets and δ-nano continuity in δ-nano topological spaces. International

Journal of Innovative Science and Research Technology 2017, Vol 2 (12), pp 110-118.

[11] Parimala, M.; Jeevitha, R.; Jafari, S.; Samarandache, F.; Karthika, M. Neutrosophic nano αψ-closed sets

in neutrosophic nano topological spaces. Journal of advance Research in Dynamical and Control Systems

2018, Vol 10, pp 523-531.

[12] Parimala, M.; Karthika, K.; Smarandache, F.; Broumi, S. On αw-closed sets and its connectedness in

terms of neutrosophic topological spaces. International Journal of Neutrosophic Sciences 2020, Vol 2, pp

82-88.

[13] Pawlak, Z. Rough sets. International Journal of Computer and Information Sciences 1982, Vol 11, pp

341-356.

[14] S. Saha, “Fuzzy δ-continuous mappings”, Journal of Mathematical Analysis and Applications, Vol 126,

pp 130-142, 1987.

[15] Salama, A.A.; Alblowi, S.A. Generalized neutrosophic set and generalized neutrosophic topological

spaces. Journal of Computer Sci. Engineering 2012, Vol 2 (7), pp 129-132.

[16] Salama, A.A.; Alblowi, S.A. Neutrosophic Set and Neutrosophic Topological Spaces. IOSR Journal of

Mathematics 2012, Vol 3 (4), pp 31-35.

[17] Smarandache, F. A unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic

probability, American Research Press, Rehoboth, NM, 1999.

[18] Smarandache, F. Neutrosophy and neutrosophic logic, First International Conference on Neutrosophy,

Neutrosophic Logic, Set, Probability, and Statistics, University of New Mexico, Gallup, NM 87301,

USA 2002.

[19] Vadivel, A.; Seenivasan, M.; John Sundar, C. An Introduction to δ-open sets in a Neutrosophic Topological

Spaces. Journal of Physics: Conference Series 2021, 1724, 012011.

[20] Vadivel, A.; John Sundar, C. Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps. International

Journal of Neutrosophic Science (IJNS) 2021, Vol 13 (2), pp 66-74.

[21] Vadivel, A.; Thangaraja, P.; John Sundar, C. Neutrosophic e-continuous maps and neutrosophic eirresolute

maps. Turkish Journal of Computer and Mathematics Education 2021, Vol 12 (1S), pp 369-375.

[22] Vadivel, A.; Thangaraja, P.; John Sundar, C. Neutrosophic e-Open Maps, Neutrosophic e-Closed Maps

and Neutrosophic e-Homeomorphisms in Neutrosophic Topological Spaces. AIP Conference Proceedings

2021, 2364, 020016.

[23] Zadeh, L.A. Fuzzy sets. Information and control 1965, Vol 8, pp 338-353.

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Vadivel, A., Sundar, C. John, Kirubadevi, K., Tamilselvan, S.. "More on Neutrosophic Nano Open Sets." International Journal of Neutrosophic Science, vol. Volume 18, no. Issue 4, 2022, pp. 204-222. DOI: https://doi.org/10.54216/IJNS.180419
Vadivel, A., Sundar, C., Kirubadevi, K., Tamilselvan, S. (2022). More on Neutrosophic Nano Open Sets. International Journal of Neutrosophic Science, Volume 18(Issue 4), 204-222. DOI: https://doi.org/10.54216/IJNS.180419
Vadivel, A., Sundar, C. John, Kirubadevi, K., Tamilselvan, S.. "More on Neutrosophic Nano Open Sets." International Journal of Neutrosophic Science Volume 18, no. Issue 4 (2022): 204-222. DOI: https://doi.org/10.54216/IJNS.180419
Vadivel, A., Sundar, C., Kirubadevi, K., Tamilselvan, S. (2022) 'More on Neutrosophic Nano Open Sets', International Journal of Neutrosophic Science, Volume 18(Issue 4), pp. 204-222. DOI: https://doi.org/10.54216/IJNS.180419
Vadivel A, Sundar C, Kirubadevi K, Tamilselvan S. More on Neutrosophic Nano Open Sets. International Journal of Neutrosophic Science. 2022;Volume 18(Issue 4):204-222. DOI: https://doi.org/10.54216/IJNS.180419
A. Vadivel, C. Sundar, K. Kirubadevi, S. Tamilselvan, "More on Neutrosophic Nano Open Sets," International Journal of Neutrosophic Science, vol. Volume 18, no. Issue 4, pp. 204-222, 2022. DOI: https://doi.org/10.54216/IJNS.180419
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