International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

Submit Your Paper

2690-6805ISSN (Online) 2692-6148ISSN (Print)
Full Length Article

International Journal of Neutrosophic Science

Volume 24 , Issue 2 , PP: 163-175, 2024 | Cite this article as | XML | Html | PDF

Foundations of neutrosophic convex structures

Jos´e Sanabria 1 * , Ennis Rosas 2 , Elvis Aponte 3

  • 1 Department of Mathematics, Faculty of Education and Sciences, University of Sucre, Sincelejo, Colombia - (jesanabri@gmail.com)
  • 2 Department of Natural and Exact Sciences, Universidad de la Costa, Barranquilla, Colombia - (ennisrafael@gmail.com)
  • 3 Department of Mathematics, Faculty of Natural Sciences and Mathematics, Escuela Superior Polit´ecnica del Litoral (ESPOL), Campus Gustavo Galindo km. 30.5 V´ıa Perimetral, Guayaquil, Ecuador - (ecaponte@espol.edu.ec)
  • Doi: https://doi.org/10.54216/IJNS.240214

    Received: October 22, 2023 Revised: February 09, 2024 Accepted: April 20, 2024
    Abstract

    In this paper an idea of neutrosophic convex structures (briefly, NC-structures) is given and some of their properties are explored. Also, NC-sets, neutrosophic concave sets and neutrosophic convex hull are defined and their properties are investigated. Moreover, the notions of NC-derived operator and NC-base are studied and their relationship to NC-structures are established.

    Keywords :

    Neutrosophic set , NC-space , neutrosophic hull operator , NC-derived operator , NC-base

    References

    [1] A.Q. Ansari, R. Biswas, S. Aggarwal, Proposal for applicability of neutrosophic set theory in medical AI, International Journal of Computer Applications 27 (2011), 5–11.

    [2] I. Arokiarani, R. Dhavaseelan, S. Jafari, M. Parimala, On some new notations and functions in neutrosophic topological spaces, Neutrosophic Sets and Systems 16 (2017), 16-19.

    [3] M. Arora, R. Biswas, U.S. Pandey, Neutrosophic relational database decomposition, International Journal of Advanced Computer Science and Applications 2 (2011), 121-125.

    [4] H.D. Cheng, Y. Guo, A new neutrosophic approach to image thresholding, New Mathematics and Natural Computation 4 (2008), 291-308.

    [5] F. Chen, C. Shen, Characterizations of convex spaces and anti-matroids via derived operators, Open Mathematics 17(1) (2019), 331-342.

    [6] S. Das, R. Das, S. Pramanik, Neutrosophic separation axioms, Neutrosophic Sets and Systems 49 (2022), 103-110.

    [7] Y. Guo, H.D. Cheng, New neutrosophic approach to image segmentation, Pattern Recognition 42 (2009), 587-595.

    [8] S. Karatas, C. Kuru, Neutrosophic topology, Neutrosophic Sets and Systems 13 (2016), 90-95.

    [9] A. Kharal, A neutrosophic multicriteria decision making method, New Mathematics and Natural Computation 10 (2014), 143-162.

    [10] G.C. Ray, S. Dey, Relation of quasi-coincidence for neutrosophic sets, Neutrosophic Sets and Systems 46 (2021), 402-415.

    [11] A.A. Salama, S.A. Alblowi, Neutrosophic set and neutrosophic topological spaces, IOSR Journal of Mathematics 3 (2012), 31-35.

    [12] F. Smarandache, A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic, American Research Press: Rehoboth, USA, 1999.

    [13] F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets, International Journal of Pure and Applied Mathematics 24 (2005), 287-297.

    [14] F. Smarandache, Foundation of revolutionary topologies: An overview, examples, trend analysis, research issues, challenges, and future directions, Neutrosophic Systems with Applications 13 (2024), 45- 66.

    [15] V.P. Soltan, d-convexity in graphs, Soviet Mathematics Doklady 28(2) (1983), 419-421.

    [16] M. Van de Vel, Binary convexities and distributive lattices, Proceedings of the London Mathematical Society, s3-48 (1984), 1-33.

    [17] M. Van de Vel, Theory of convex structures, North-Holland Mathematical Library: Amsterdan, The Netherlands, 1993.

    [18] J. Van Mill, Supercompactness and Wallman Spaces, Mathematisch Centrum: Amsterdam, The Netherlands, 1997.

    [19] M. Zhang, L. Zhang, H.D. Cheng, A neutrosophic approach to image segmentation based on watershed method, Signal Processing 90(5) (2010), 1510-1517.

    Cite This Article As :
    Jos´e Sanabria, Ennis Rosas, Elvis Aponte. "Foundations of neutrosophic convex structures." Full Length Article, Vol. 24, No. 2, 2024 ,PP. 163-175 (Doi   :  https://doi.org/10.54216/IJNS.240214)
    Jos´e Sanabria, Ennis Rosas, Elvis Aponte. (2024). Foundations of neutrosophic convex structures. Journal of , 24 ( 2 ), 163-175 (Doi   :  https://doi.org/10.54216/IJNS.240214)
    Jos´e Sanabria, Ennis Rosas, Elvis Aponte. "Foundations of neutrosophic convex structures." Journal of , 24 no. 2 (2024): 163-175 (Doi   :  https://doi.org/10.54216/IJNS.240214)
    Jos´e Sanabria, Ennis Rosas, Elvis Aponte. (2024). Foundations of neutrosophic convex structures. Journal of , 24 ( 2 ), 163-175 (Doi   :  https://doi.org/10.54216/IJNS.240214)
    Jos´e Sanabria, Ennis Rosas, Elvis Aponte. Foundations of neutrosophic convex structures. Journal of , (2024); 24 ( 2 ): 163-175 (Doi   :  https://doi.org/10.54216/IJNS.240214)
    Jos´e Sanabria, Ennis Rosas, Elvis Aponte, Foundations of neutrosophic convex structures, Journal of , Vol. 24 , No. 2 , (2024) : 163-175 (Doi   :  https://doi.org/10.54216/IJNS.240214)