Volume 26 • Issue 1 • PP: 283-292 • 2025
Neutrosophic subgroups and neutrosophic normal subgroups of groups
Open Access & Copyright
© 2025 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, we introduce the concepts of neutrosophic subgroups and neutrosophic normal subgroups of groups and investigate several properties. We investigate relations between neutrosophic subgroups (neutrosophic normal subgroups) and their neutrosophic level subsets of a group. We also look at the homomorphic image and inverse image of the neutrosophic subgroups and neutrosophic normal subgroups of groups, as well as some related properties.
Keywords
References
[1] N. Ajmal and A. S. Prajapati, Fuzzy cosets and fuzzy normal subgroups, Inf. Sci., 64(1), (1992), 17-25. https://doi.org/10.1016/0020-0255(92)90107-J
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1), (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
[3] S. Bhunia, G. Ghorai and Q. Xin, On the characterization of neutrosophic subgroups, AIMS Math., 6(1), (2021), 962-978. https://doi.org/10.3934/math.2021058
[4] S. Bhunia and G. Ghorai, An approach to Lagrange’s theorem in Pythagorean fuzzy subgroups, Kragujevac J. Math., 48(6), (2024), 893-906.
[5] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer-Verlag, New York, 2005.
[6] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35(3), (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
[7] R. L. Roth, A history of Lagrange’s theorem on groups, Math. Mag., 74(2), (2001), 99-108. https: //doi.org/10.1080/0025570X.2001.11953045
[8] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics (fourth edition), American Research Press, Rehoboth, 2005.
[9] F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24(3), (2005), 287-297.
[10] V. Cetkin and H. Aygun, An approach to neutrosophic subgroup and its fundamental properties, J. Intell. Fuzzy Syst., 29, (2015), 1941-1947. https://doi.org/10.3233/IFS-151672
[11] R. R. Yager, Pythagorean fuzzy subsets, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, AB, Canada, 2013, 57-61. https://doi.org/10.1109/ IFSA-NAFIPS.2013.6608375
[12] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
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.