Volume 26 • Issue 2 • PP: 55-66 • 2025
Lagrange’s theorem based on neutrosophic sets
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).
Abstract
This paper explores the fundamental concepts of sub-level subgroups, element orders, normalizers, and centralizers within the framework of neutrosophic group theory. Additionally, it examines quotient groups and the index of a subgroup, extending classical algebraic structures to a neutrosophic setting. Finally, a generalized formulation of Lagrange’s theorem is presented, demonstrating its applicability in the neutrosophic environment and highlighting its implications for uncertain and indeterminate group structures.
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] A. Al-Odhari, Characteristics neutrosophic subgroups of axiomatic neutrosophic groups, Neutrosophic Optimization and Intelligent Systems, 3 (2024), 32-40. https://doi.org/10.61356/j.nois. 2024.3265
[3] K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst., 20(1) (1986), 87-96. https://doi.org/ 10.1016/S0165-0114(86)80034-3
[4] 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
[5] S. Bhunia, G. Ghorai and Q. Xin. On the fuzzification of Lagrange’s theorem in (α, β)-Pythagorean fuzzy environment, AIMS Math., 6(9) (2021), 9290-9308. https://doi.org/10.3934/math. 2021540
[6] S. Bhunia and G. Ghorai, An approach to Lagrange’s theorem in Pythagorean fuzzy subgroups, Kragujevac J. Math., 48(6) (2024), 893-906.
[7] 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
[8] A. Iampan, C. Sivakumar and N. Rajesh, Neutrosophic subgroups and neutrosophic normal subgroups of groups, Int. J. Neutrosophic Sci., 26(1) (2025), 283-292. https://doi.org/10.54216/IJNS. 260124
[9] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy Group Theory, Springer-Verlag, New York, 2005.
[10] A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35(3) (1971), 512-517. https://doi.org/10. 1016/0022-247X(71)90199-5
[11] 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
[12] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability and statistics (fourth edition), American Research Press, Rehoboth, 2005.
[13] S. Thiruveni and A. Solairaju, Neutrosophic Q-fuzzy subgroups, Int. J. Math. And Appl., 6(1) (2018), 859-866.
[14] 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
[15] 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.