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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 25 , Issue 4 , PP: 433-443, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Neutrosophic N-structures on Sheffer stroke UP-algebras

S. R. Vidhya 1 , Aiyared Iampan 2 * , Neelamegarajan Rajesh 3

  • 1 Department of Mathematics, Bon Secours College for Women (affiliated to Bharathidasan University), Thanjavur-613006, Tamil Nadu, India - (svsubi16@gmail.com)
  • 2 Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Mae Ka, Mueang, Phayao 56000, Thailand - (aiyared.ia@up.ac.th)
  • 3 Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathdasan University), Thanjavur-613005, Tamil Nadu, India - (nrajesh topology@yahoo.co.in)

    • Doi: https://doi.org/10.54216/IJNS.250437

    Received: October 12, 2024 Revised: November 27, 2024 Accepted: January 19, 2025
    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.

    Cite This Article As :
    R., S.. , Iampan, Aiyared. , Rajesh, Neelamegarajan. Neutrosophic N-structures on Sheffer stroke UP-algebras. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 433-443. DOI: https://doi.org/10.54216/IJNS.250437
    R., S. Iampan, A. Rajesh, N. (2025). Neutrosophic N-structures on Sheffer stroke UP-algebras. International Journal of Neutrosophic Science, (), 433-443. DOI: https://doi.org/10.54216/IJNS.250437
    R., S.. Iampan, Aiyared. Rajesh, Neelamegarajan. Neutrosophic N-structures on Sheffer stroke UP-algebras. International Journal of Neutrosophic Science , no. (2025): 433-443. DOI: https://doi.org/10.54216/IJNS.250437
    R., S. , Iampan, A. , Rajesh, N. (2025) . Neutrosophic N-structures on Sheffer stroke UP-algebras. International Journal of Neutrosophic Science , () , 433-443 . DOI: https://doi.org/10.54216/IJNS.250437
    R. S. , Iampan A. , Rajesh N. [2025]. Neutrosophic N-structures on Sheffer stroke UP-algebras. International Journal of Neutrosophic Science. (): 433-443. DOI: https://doi.org/10.54216/IJNS.250437
    R., S. Iampan, A. Rajesh, N. "Neutrosophic N-structures on Sheffer stroke UP-algebras," International Journal of Neutrosophic Science, vol. , no. , pp. 433-443, 2025. DOI: https://doi.org/10.54216/IJNS.250437

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