Volume 24 , Issue 2 , PP: 163-175, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Jos´e Sanabria 1 * , Ennis Rosas 2 , Elvis Aponte 3
Doi: https://doi.org/10.54216/IJNS.240214
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.
Neutrosophic set , NC-space , neutrosophic hull operator , NC-derived operator , NC-base
[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.
