Volume 24 • Issue 2 • PP: 163-175 • 2024
Foundations of neutrosophic convex structures
Open Access & Copyright
© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF 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
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
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.