International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 13 , Issue 2 , PP: 66-74, 2021 | Cite this article as | XML | PDF | Full Length Article

Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps

A. Vadivel 1 * , C. John Sundar 2

  • 1 PG and Research Department of Mathematics, Government Arts College (Autonomous), Karur - 639 005, India - (avmaths@gmail.com)
  • 2 Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India - (johnphdau@hotmail.com)
  • Doi: https://doi.org/10.54216/IJNS.130203

    Received:Octobre 30, 2020 Accepted: January 20, 2021
    Abstract

    The neutrosophic δ-open set is one of the strongest forms of neutrosophic topological spaces. In this article, we introduce the concept of neutrosophic δ-open maps and neutrosophic δ-closed maps and investigate their neighbor maps such as δS, δp & e* open maps and closed maps of neutrosophic topological spaces. Also, we analyze some of their related properties and extension to neutrosophic e*- homeomorphism and neutrosophic e* T½-space in neutrosophic topological spaces. Furthermore, these kinds of δ-open functions have strong application in the area of neural networks and image processing theory. 

    Keywords :

    neutrosophic &delta , -open map, neutrosophic &delta , -closed map, neutrosophic  , e*-open map, neutrosophic  , e*-closed map, neutrosophic  , e* T½ , -space  , , neutrosophic  , e*-homeomorphism

    References

     

    [1] Al-Hamido, R.K., “A New Approach Of Neutrosophic Topological space”, International Journal of Neutrosophic Science, Vol 7, pp 55-61, 2020.

    [2] Al-Omeri, W., “Neutrosophic crisp sets via neutrosophic crisp topological spaces” Neutrosophic Sets System, Vol 13, pp 96-104, 2016.

    [3] Al-Omeri, W., and Jafari, S., “On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces”, Mathematics, Vol 7, pp 1-12, 2018.

    [4] Al-Omeri, W.F., and Jafari, S., “Neutrosophic pre-continuous multifunctions and almost pre-continuous multifunctions”, Neutrosophic Sets and Systems, Vol 27, pp 53-69, 2019.

    [5] Arokiarani, I., Dhavaseelan, R., Jafari, S., and Parimala, M., “On some new notions and functions in neutrosophic topological space”, Neutrosophic Sets and Systems, Vol 16, pp 16-19, 2017.

    [6] Atanassov, K., and Stoeva, S., “Intuitionistic fuzzy sets”, Proc. of Polish Symp. on Interval and Fuzzy Mathematics, Poznan, pp 23-26, 1983.

    [7] Atanassov, K., “Intuitionistic fuzzy sets”, Fuzzy Sets and Syst., Vol 20, pp 87-96, 1986.

     

    [8] Atanassov, K., “Review and new results on intuitionistic fuzzy sets”, Mathematical Foundations of Artificial Intelligence Semin, Preprint IM-MFAIS, Sofia, pp 1-88, 1988.

    [9] Chang, C.L., “Fuzzy topological space”, J. Math. Anal. Appl., Vol 24, pp 182-190, 1968.

     [10] Coker, D., “An introduction to intuitionistic fuzzy topological spaces”, Fuzzy sets and syst., Vol 88, pp 81-89, 1997.

    [11] Krishna Prabha, S., Said Broumi, and Seluk Topal, “A Novel Routing Network Algorithm via Netrosophic Fuzzy Set Approach”, International Journal of Neutrosophic Science, Vol 13, pp 9-22, 2021.

    [12] Parimala, M., Jeevitha, R., Smarandache, F., Jafari, S., and Udhayakumar, R., “Neutrosophic -homeomorphism in Neutrosophic Topological Spaces”, Information, Vol 9 (187), pp 1-10, 2018.

    [13] Parimala, M., Karthika, M., and Smarandache, F., “A Review of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces and Neutrosophic Soft Topological Spaces”, International Journal of Neutrosophic Science, Vol 10, pp 96-104, 2020.

     

    [14] Salama, A.A., and Smarandache, F., “Neutrosophic crisp set theory”, Educational Publisher, Columbus, Ohio, USA, 2015.

    [15] Salama, A.A., and Alblowi, S.A., “Neutrosophic set and neutrosophic topological spaces”, IOSR Journal of Mathematics, Vol 3, pp 31-35, 2012.

    [16] Salama, A.A., Smarandache, F., and Alblowi, S.A, “Characteristic function of neutrosophic set”, Neutrosophic Sets and Systems, Vol 3, pp 14-17, 2014.

    [17] Salama, A.A., Smarandache, F., and Kromov, V., “Neutrosophic closed set and neutrosophic continuous functions”, Neutrosophic Sets and Systems, Vol 4, pp 4-8, 2014.

    [18] Salama, A.A., ElGhawalby, H., and Nasr, A.M., “Star Neutrosophic Fuzzy Topological Space”, International Journal of Neutrosophic Science, Vol 0, pp 77-82, 2019.

    [19] Smarandache, F., “A Unifying field in logics: neutrosophic logic. neutrosophy, Nss, neutrosophic probability”, American Research Press, Rehoboth, NM, 1999.

    [20] 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.

    [21] Smarandache, F., and Pramanik, S., “New Neutrosophic Sets via Neutrosophic Topological Spaces”, Neutrosophic Operational Research, Pons Editions: Brussels, Belgium, Vol I, pp. 189209, 2017.

    [22] Saha, S., “Fuzzy _-continuous maps”, J. Math. Anal. Appl., Vol 126, pp 130-142, 1987.

    [23] Vadivel, A., Seenivasan, M., and John Sundar, C., “An Introduction to -open sets in a Neutrosophic Topological Spaces”, Journal of Physics: Conference Series, 1724, 012011, 2021.

    [24] Zadeh, L.A., “Fuzzy sets”, Inform. Control, Vol 8, pp 338-353, 1965.

     

    Cite This Article As :
    Vadivel, A.. , John, C.. Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps. International Journal of Neutrosophic Science, vol. , no. , 2021, pp. 66-74. DOI: https://doi.org/10.54216/IJNS.130203
    Vadivel, A. John, C. (2021). Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps. International Journal of Neutrosophic Science, (), 66-74. DOI: https://doi.org/10.54216/IJNS.130203
    Vadivel, A.. John, C.. Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps. International Journal of Neutrosophic Science , no. (2021): 66-74. DOI: https://doi.org/10.54216/IJNS.130203
    Vadivel, A. , John, C. (2021) . Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps. International Journal of Neutrosophic Science , () , 66-74 . DOI: https://doi.org/10.54216/IJNS.130203
    Vadivel A. , John C. [2021]. Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps. International Journal of Neutrosophic Science. (): 66-74. DOI: https://doi.org/10.54216/IJNS.130203
    Vadivel, A. John, C. "Neutrosophic δ-Open Maps and Neutrosophic δ-Closed Maps," International Journal of Neutrosophic Science, vol. , no. , pp. 66-74, 2021. DOI: https://doi.org/10.54216/IJNS.130203