Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets

M.; M. Mary

doi:https://doi.org/10.54216/IJNS.260108

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Volume 26 • Issue 1 • PP: 94-107 • 2025

Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets

M. Mala ^1*

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,

M. Mary Jansirani ²

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¹Research Scholar, School of Sciences, Division of Mathematics, SRM- Institute of Science and Technology; Tiruchirappalli Campus, SRM Nagar, Trichy – Chennai Highway, Near Samayapuram, Tiruchi

²Associate Professor, School of Sciences, Division of Mathematics, SRM- Institute of Science and Technology; Tiruchirappalli Campus, SRM Nagar, Trichy – Chennai Highway, Near Samayapuram, Tiru

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.260108

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Received: October 22, 2024 Revised: January 15, 2025 Accepted: February 18, 2025

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Abstract

This paper introduces the concept of -(3,2) ƒuzzy ᵴemigroups within an -ᵴemigroup and explore their characterizations. Various comparable conditions for -(3,2) ƒuzzy normal subᵴemigroups are established. Additionally, the -(3,2) ƒuzzy coset, -(3,2) ƒuzzy ideal, -(3,2) ƒuzzy symmetric ᵴemigroup and -(3,2) ƒuzzy normal subᵴemigroups are defined. The idea of conjugate -(3,2) ƒuzzy ᵴemigroups is also introduced, and the order of an -(3,2) ƒuzzy ᵴemigroup is determined. The (3,2) ƒuzzy semigroup condition applied to decision making process also.

Keywords

-ᵴemigroups[SSG] -&fnof uzzy ᵴemigroups[SFSG] -&fnof uzzy normal subᵴemigroup[SFNSG] -(3 2) &fnof uzzy ᵴemigroups[S(3 2)FSG] -non (3 2) &fnof uzzy ᵴemigroups[SN(3 2)FSG] &nbsp - strong (3 2) &fnof uzzy ᵴemigroups[SS(3 2)FSG] -(3 2) &fnof uzzy normal subᵴemigroups[S(3 2)FNSSG] -(3 2) &fnof uzzy Ideals [S(3 2)FI] -(3.2) &fnof uzzy hyper subᵴemigroup[S(3 2)FHSSG] -(3 2) &fnof uzzy subᵴemigroup[S(3 2)FSSG] -conjugate (3 2) &fnof uzzy subᵴemigroups[SC(3 2)FSSG] -(3 2) &fnof uzzy symmetric ᵴemigroup[S(3 2)FSYSG] &nbsp -(3 2) &fnof uzzy coset [S(3 2)FC]

References

[1] L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, no. 3, pp. 338–353, 1965.

[2] A. Rosenfeld, "Fuzzy groups," Journal of Mathematical Analysis and Applications, vol. 35, pp. 512–517, 1971.

[3] F. Smarandache, Special Algebraic Structures in Collected Papers, vol. III, Abaddaba, Oradea: American Research Press, 2000, pp. 78–81.

[4] W. B. V. Kandasamy, Smarandache Semigroups, Rehoboth, NM: American Research Press, 2002.

[5] W. B. V. Kandasamy, Smarandache Fuzzy Algebra, Rehoboth, NM: American Research Press, 2003.

[6] H. R. Yassein and M. O. Karim, "On Smarandache M-semigroup," Journal of Al-Qadisiya for Pure Science, vol. 3, no. 1, pp. 71–76, 2011.

[7] A. P. J. Allen, H. S. Kim, and J. Neggers, "Smarandache algebras and their subgroups," Bulletin of the Iranian Mathematical Society, vol. 38, no. 4, pp. 1063–1077, 2012.

[8] R. R. Yager, "Pythagorean fuzzy subsets," in Proc. 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, Canada, 2013, pp. 57–61.

[9] S. K. Mohammed, "Some results on Smarandache semigroups," Journal of Kufa for Mathematics and Computer, vol. 1, no. 7, pp. 33–36, Dec. 2013.

[10] M. Ali, "Smarandache soft semigroups and their properties," Journal of New Theory, vol. 1, pp. 80–88, 2015.

[11] R. Gowri and T. Rajeswari, "S-α fuzzy semigroups," International Journal of Mathematical Sciences and Engineering Applications, vol. 9, no. 1, pp. 307–318, Mar. 2015.

[12] R. A. Doss and S. Suganya, "Smarandache Q-fuzzy semigroups," Advances in Fuzzy Mathematics (AFM), vol. 11, no. 1, pp. 89–97, 2016.

[13] R. Gowri and T. Rajeswari, "Smarandache-alpha fuzzy normal subsemigroups in Smarandache-alpha fuzzy semigroups," Proceedings of the National Academy of Sciences, India, Section A: Physical Sciences, vol. 90, pp. 777–781, 2020.

[14] H. Z. Ibrahim, T. M. Al-Shami, and O. G. Elbarbary, "(3,2)-Fuzzy sets and their applications to topology and optimal choices," Computational Intelligence and Neuroscience, vol. 2021, no. 1, 2021.

[15] A. Iampan, N. Rajesh, and S. Shanthi, "Abelian subgroups based on (3, 2)-fuzzy sets," IAENG International Journal of Computer Science, vol. 49, no. 3, Sep. 2022.

[16] M. Vanishri, N. Rajesh, N. Rafi, and R. Bandaru, "Ideal theory of semigroups based on (3, 2)-fuzzy sets," Journal of Mathematics and Computer Science, vol. 28, pp. 182–191, 2023.

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Mala, M., Jansirani, M. Mary. "Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets." International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 1, 2025, pp. 94-107. DOI: https://doi.org/10.54216/IJNS.260108

Mala, M., Jansirani, M. (2025). Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets. International Journal of Neutrosophic Science, Volume 26(Issue 1), 94-107. DOI: https://doi.org/10.54216/IJNS.260108

Mala, M., Jansirani, M. Mary. "Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets." International Journal of Neutrosophic Science Volume 26, no. Issue 1 (2025): 94-107. DOI: https://doi.org/10.54216/IJNS.260108

Mala, M., Jansirani, M. (2025) 'Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets', International Journal of Neutrosophic Science, Volume 26(Issue 1), pp. 94-107. DOI: https://doi.org/10.54216/IJNS.260108

Mala M, Jansirani M. Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets. International Journal of Neutrosophic Science. 2025;Volume 26(Issue 1):94-107. DOI: https://doi.org/10.54216/IJNS.260108

M. Mala, M. Jansirani, "Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets," International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 1, pp. 94-107, 2025. DOI: https://doi.org/10.54216/IJNS.260108

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