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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 25 • Issue 4 • PP: 433-443 • 2025

Neutrosophic N-structures on Sheffer stroke UP-algebras

S. R. Vidhya 1*
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,
Aiyared Iampan 2
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,
Neelamegarajan Rajesh 3
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1Department of Mathematics, Bon Secours College for Women (affiliated to Bharathidasan University), Thanjavur-613006, Tamil Nadu, India
2Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Mae Ka, Mueang, Phayao 56000, Thailand
3Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathdasan University), Thanjavur-613005, Tamil Nadu, India
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.250437
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Received: October 12, 2024 Revised: November 27, 2024 Accepted: January 19, 2025
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Abstract

The study defines a neutrosophic N-subalgebra and a level set of a neutrosophic N-structure on Sheffer stroke UP-algebras. It appears that these concepts are integral to understanding the behavior of neutrosophic logic within the framework of Sheffer stroke UP-algebras. The study establishes a relationship between subalgebras and level sets on Sheffer stroke UP-algebras. Specifically, it proves that the level set of neutrosophic Nsubalgebras on this algebra is its subalgebra, and vice versa. This indicates a tight connection between these concepts within the given algebraic structure. It is stated that the family of all neutrosophic N-subalgebras of a Sheffer stroke UP-algebra forms a complete distributive lattice. This suggests that there is a well-defined structure and order among these subalgebras, allowing for systematic analysis. The study describes a neutrosophic N-ideal of a Sheffer stroke UP-algebra and provides some of its properties. Additionally, it is shown that every neutrosophic N-ideal of a Sheffer stroke UP-algebra is also its neutrosophic N-subalgebra, though the inverse is generally not true. This highlights the specific characteristics and behavior of neutrosophic Nideals within the given algebraic context.

Keywords

Sheffer stroke UP-algebra Subalgebra Ideal Neutrosophic N-subalgebra Neutrosophic N-ideal

References

[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20(1), (1986), 87-96.

[2] A. Iampan, A new branch of the logical algebra: UP-algebras, J. Algebra Relat. Top., 5(1), (2017), 35-54.

[3] M. K. Shrimali and S. K. Sharma, ”Sheffer Stroke Hilbert Algebras Stabilizing by Ideals,” Axioms, vol. 13, no. 2, p. 97, 2024.

[4] M. Khan, S. Anis, F. Smarandache, Y. B. Jun, Neutrosophic N-structures and their applications in semigroups, Ann. Fuzzy Math. Inform., 14(6), (2017), 583-598.

[5] T. Oner and T. Katican, On ideals of Sheffer stroke UP-algebras, J. Discrete Math. Sci. Cryptogr., 26(8), (2023), 2257-2271.

[6] T. Oner and T. Katican, On Sheffer stroke UP-algebras, Discuss. Math., Gen. Algebra Appl., 41, (2021), 381-394.

[7] P. Rangsuk, P. Huana, A. Iampan, NeutrosophicN-structures over UP-algebras, Neutrosophic Sets Syst., 28, (2019), 87-127.

[8] H. M. Sheffer, A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Am. Math. Soc., 14(4), (1913), 481-488.

[9] F. Smarandache, A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability (fourth edition), Rehoboth American Research Press, 2008.

[10] F. Smarandache, Neutrosophic set — a generalization of the intuitionistic fuzzy set, 2006 IEEE International Conference on Granular Computing, (2006), 38-42.

[11] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), (1965), 338-353.

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format_quote
Vidhya, S. R., Iampan, Aiyared, Rajesh, Neelamegarajan. "Neutrosophic N-structures on Sheffer stroke UP-algebras." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, 2025, pp. 433-443. DOI: https://doi.org/10.54216/IJNS.250437
Vidhya, S., Iampan, A., Rajesh, N. (2025). Neutrosophic N-structures on Sheffer stroke UP-algebras. International Journal of Neutrosophic Science, Volume 25(Issue 4), 433-443. DOI: https://doi.org/10.54216/IJNS.250437
Vidhya, S. R., Iampan, Aiyared, Rajesh, Neelamegarajan. "Neutrosophic N-structures on Sheffer stroke UP-algebras." International Journal of Neutrosophic Science Volume 25, no. Issue 4 (2025): 433-443. DOI: https://doi.org/10.54216/IJNS.250437
Vidhya, S., Iampan, A., Rajesh, N. (2025) 'Neutrosophic N-structures on Sheffer stroke UP-algebras', International Journal of Neutrosophic Science, Volume 25(Issue 4), pp. 433-443. DOI: https://doi.org/10.54216/IJNS.250437
Vidhya S, Iampan A, Rajesh N. Neutrosophic N-structures on Sheffer stroke UP-algebras. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 4):433-443. DOI: https://doi.org/10.54216/IJNS.250437
S. Vidhya, A. Iampan, N. Rajesh, "Neutrosophic N-structures on Sheffer stroke UP-algebras," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, pp. 433-443, 2025. DOI: https://doi.org/10.54216/IJNS.250437
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