Journal of Neutrosophic and Fuzzy Systems

Journal DOI

https://doi.org/10.54216/JNFS

Submit Your Paper

2771-6449ISSN (Online) 2771-6430ISSN (Print)

Volume 10 , Issue 1 , PP: 25-33, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Neutrosophic Boundary and Neutrosophic Semi-boundary on Fuzzy Setting

E. Poongothai 1 , E. Kalaivani 2

  • 1 Associate Professor, PG & Research Department of Mathematics, Shanmuga Industries Arts and Science College, Tiruvannamalai-606603, Tamilnadu, India - (epoongothai5@gmail.com)
  • 2 Ph.D(Full-time) Research Scholar, PG & Research Department of Mathematics, Shanmuga Industries Arts and Science College, Tiruvannamalai-606 603, Tamilnadu, India - (kalai12feb@gmail.com)
  • Doi: https://doi.org/10.54216/JNFS.100103

    Received: November 09, 2024, Revised: December 14, 2024 Accepted: January 03, 2025
    Abstract

    The aim of this paper is to introduce the concept of fuzzy neutrosophic boundary and fuzzy neutrosophic semi-boundary of a fuzzy neutrosophic topological space. Some characterization are discussed. Several examples and properties are obtained.The aim of this paper is to introduce the concept of fuzzy neutrosophic boundary and fuzzy neutrosophic semi-boundary of a fuzzy neutrosophic topological space. Some characterization are dis- cussed.Several examples and properties are obtained.

    Keywords :

    Fuzzy neutrosophic open , Fuzzy neutrosophic closed , Fuzzy neutrosophic semi-open , Fuzzzy neutrosophic semi-closed , Fuzzy neutrosophic semi-interior , Fuzzy neutrosophic semi-closure , Fuzzy neutrosophic boundary , Fuzzy neutrosophic semi-boundary

    References

    [1]       S. A. Alblowi, A. A. Salama, and M. Eisa, “New concepts of neutrosophic sets,” International Journal of Mathematics and Computer Application Research (IJMCAR), vol. 3, no. 3, pp. 95–102, Oct. 2013.

     

    [2]       M. Alimohammady and M. Roohi, “Fuzzy minimal structure and Fuzzy minimal vector spaces,” Chaos, Solitons and Fractals, vol. 27, no. 3, pp. 599–605, 2006.

     

    [3]       B. Ahmad and M. Athar, “Fuzzy set open and closed function,” submitted.

     

    [4]       M. Athar and B. Ahmad, “Fuzzy boundary and fuzzy semiboundary,” Advances in Fuzzy Systems, vol. 2008, Art. no. 586893, 9 pages, 2008.

     

    [5]       I. Arockiarani and J. J. Martina, “More on fuzzy neutrosophic sets and fuzzy neutrosophic topological spaces,” International Journal of Innovative Research and Studies, vol. 3, no. 5, pp. 643–652, 2014.

     

    [6]       K. K. Azad, “On Fuzzy semi continuity; Fuzzy almost continuity and Fuzzy weakly continuity,” Journal of Mathematical Analysis and Applications, vol. 82, no. 1, pp. 14–32, 1981.

     

    [7]       G. Balasubramanian, “On Fuzzy pre-separation axioms,” Bulletin of the Calcutta Mathematical Society, vol. 90, no. 6, pp. 427–434, 1998.

     

    [8]       C. L. Chang, “Fuzzy topological spaces,” Journal of Mathematical Analysis and Applications, vol. 24, no. 1, pp. 182–190, 1968.

     

    [9]       M. J. Egenhofer and R. D. Franzosa, “Point-set topological spatial relations,” International Journal of Geographical Information Science, vol. 5, no. 2, pp. 161–174, 1991.

     

    [10]    M. J. Egenhofer and J. Herring, “Categorizing binary topological relations between regions, lines and points in geographic databases,” Department of Surveying Engineering, University of Maine, Orono, ME, USA, Tech. Rep., 1991.

     

    [11]    M. S. El Naschie, “On the uncertainty of Cantorian geometry and the two-slit experiment,” Chaos, Solitons and Fractals, vol. 9, no. 3, pp. 517–529, 1998.

     

    [12]    M. S. El Naschie, “On the unification of heterotic strings, M theory and $\mathcal{E}^{(\infty)}$ theory,” Chaos, Solitons and Fractals, vol. 11, no. 14, pp. 2397–2408, 2000.

     

    [13]    F. Smarandache, “Neutrosophy and Neutrosophic Logic,” in Proc. First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and Statistics, University of New Mexico, Gallup, NM, USA, 2002.

     

    [14]    J. Smith and L. Johnson, “Applications of Neutrosophic Logic in Decision-Making Processes,” Journal of Decision Systems, vol. 30, no. 1, pp. 22–35, 2022.

     

    [15]    I. M. Hanafy, A. A. Salama, and K. M. Mahfouz, “Neutrosophic Classical Events and its probability,” International Journal of Mathematics and Computer Applications Research (IJMCAR), vol. 3, no. 1, pp. 171–178, Mar. 2013.

     

    [16]    R. C. Haworth and R. A. McCoy, “Baire spaces,” Dissertationes Mathematicae, vol. 141, pp. 1–77, 1977.

     

    [17]    A. K. Katsaras and D. B. Liu, “Fuzzy vector spaces and fuzzy topological vector spaces,” Journal of Mathematical Analysis and Applications, vol. 58, no. 1, pp. 135–146, 1977.

     

    [18]    T. Krsteska, “A note on mappings of Baire spaces,” Mathematica Slovaca, vol. 27, no. 2, pp. 173–176, 1977.

     

    [19]    S. J. Lee and E. P. Lee, “Fuzzy r-continuous and fuzzy r-semi continuous maps,” International Journal of Mathematics and Mathematical Sciences, vol. 27, no. 1, pp. 53–63, 2001.

     

    [20]    [20] N. Levine, “An introduction to fuzzy neutrosophic topological spaces,” The American Mathematical Monthly, vol. 70, no. 1, pp. 36–41, 2017.

     

    [21]    M. N. Mukherjee and S. P. Sinha, “Irresolute and almost open functions between fuzzy topological spaces,” Fuzzy Sets and Systems, vol. 29, no. 3, pp. 381–388, 1989.

     

    [22]    E. Poongothai and E. Padmavathi, “On fuzzy neutrosophic semi-open (closed) sets in fuzzy neutrosophic topological spaces,” International Journal of Novel Research and Development (IJNRD), vol. 9, pp. 571–577, 2024.

     

    [23]    P. M. Pu and Y. M. Liu, “Fuzzy topology-1: neighbourhood structure of a fuzzy point and Moore-Smith convergence,” Journal of Mathematical Analysis and Applications, vol. 76, no. 2, pp. 571–599, 1980.

     

    [24]    A. Rosenfeld, “Digital topology,” The American Mathematical Monthly, vol. 86, no. 8, pp. 621–630, 1979.

     

    [25]    X. Tang, “Spatial object modeling in fuzzy topological spaces with applications to land cover change in China,” Ph.D. dissertation, University of Twente, Enschede, The Netherlands, 2004.

     

    [26]    V. Veereswari, “An introduction to fuzzy neutrosophic topological spaces,” International Journal of Mathematics and Applications (IJMA), vol. 8, no. 3, pp. 144–149, 2017.

     

    [27]    L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965.

    Cite This Article As :
    Poongothai, E.. , Kalaivani, E.. Neutrosophic Boundary and Neutrosophic Semi-boundary on Fuzzy Setting. Journal of Neutrosophic and Fuzzy Systems, vol. , no. , 2025, pp. 25-33. DOI: https://doi.org/10.54216/JNFS.100103
    Poongothai, E. Kalaivani, E. (2025). Neutrosophic Boundary and Neutrosophic Semi-boundary on Fuzzy Setting. Journal of Neutrosophic and Fuzzy Systems, (), 25-33. DOI: https://doi.org/10.54216/JNFS.100103
    Poongothai, E.. Kalaivani, E.. Neutrosophic Boundary and Neutrosophic Semi-boundary on Fuzzy Setting. Journal of Neutrosophic and Fuzzy Systems , no. (2025): 25-33. DOI: https://doi.org/10.54216/JNFS.100103
    Poongothai, E. , Kalaivani, E. (2025) . Neutrosophic Boundary and Neutrosophic Semi-boundary on Fuzzy Setting. Journal of Neutrosophic and Fuzzy Systems , () , 25-33 . DOI: https://doi.org/10.54216/JNFS.100103
    Poongothai E. , Kalaivani E. [2025]. Neutrosophic Boundary and Neutrosophic Semi-boundary on Fuzzy Setting. Journal of Neutrosophic and Fuzzy Systems. (): 25-33. DOI: https://doi.org/10.54216/JNFS.100103
    Poongothai, E. Kalaivani, E. "Neutrosophic Boundary and Neutrosophic Semi-boundary on Fuzzy Setting," Journal of Neutrosophic and Fuzzy Systems, vol. , no. , pp. 25-33, 2025. DOI: https://doi.org/10.54216/JNFS.100103