Bipolar Fuzzy Magnified Translation of Γ-Near Rings

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DOI: https://doi.org/10.28924/2291-8639-23-2025-80
Published: Mar 31, 2025
Cite as:
V. P. Vineela Korada, S. Ragamayi, Aiyared Iampan, Bipolar Fuzzy Magnified Translation of Γ-Near Rings, Int. J. Anal. Appl., 23 (2025), 80.

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V. P. Vineela Korada, S. Ragamayi, Aiyared Iampan

Abstract

This study introduces the concept of bipolar fuzzy magnified translations of Γ-near rings (BF-MT-GNRs), extending the application of bipolar fuzzy set theory within Γ-near rings. The research establishes a one-to-one correspondence between BF-MT-GNRs and bipolar fuzzy sub-GNRs, ideals, and bi-ideals, offering a deeper understanding of these algebraic structures. Furthermore, homomorphisms on BF-MT-GNRs are explored to demonstrate their structural properties and theoretical consistency. These findings contribute significantly to the ongoing development of bipolar fuzzy set theory and its applications in advanced algebraic frameworks. In alignment with Sustainable Development Goal 4 (SDG 4) on Quality Education, this study promotes mathematical literacy and critical thinking by providing new perspectives on algebraic structures that can be incorporated into school and university curricula. By making abstract mathematical concepts more accessible to students, this research fosters inclusive and equitable learning opportunities, empowering both educators and learners in their pursuit of higher-level mathematical knowledge. Moreover, the results serve as a valuable resource for researchers, facilitating further studies in algebraic systems with applications in computational mathematics, cryptography, and decision-making models. Ultimately, this work supports the global effort to enhance education at all levels, ensuring that students acquire the skills necessary for future academic and professional success.

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References

  1. H.A. Alshehri, Fuzzy Translation and Fuzzy Multiplication in BRK-Algebras, Eur. J. Pure Appl. Math. 14 (2021), 737–745. https://doi.org/10.29020/nybg.ejpam.v14i3.3971.
  2. G.L. Booth, A Note on Γ-Near Rings, Stud. Sci. Math. Hungar. 23 (1988), 471–475.
  3. Y.B. Jun, M. Sapanic, M.A. Öztürk, Fuzzy Ideals in Gamma Near-Rings, Turk. J. Math. 22 (1998), 449–459.
  4. K.J. Lee, Bipolar Fuzzy Subalgebras and Bipolar Fuzzy Ideals of BCK/BCI-Algebras, Bull. Malays. Math. Sci. Soc. 32 (2009), 361–373. https://eudml.org/doc/45571.
  5. K.M. Lee, Bipolar-Valued Fuzzy Sets and Their Operations, in: Proceedings of International Conference on Intelligent Technologies, Bangkok, Thailand, (2000).
  6. S.K. Majumdar, S.K. Sardar, Fuzzy Magnified Translation on Groups, J. Math. North Bengal Univ. 1 (2008), 117–124.
  7. S. Ragamayi, Y. Bhargavi, A Study of Vague Gamma-Near Rings, Int. J. Sci. Technol. Res. 9 (2020), 3960–3963.
  8. S. Ragamayi, Y. Bhargavi, Some Results on Homomorphism of Vague Ideal of a Gamma-Near Ring, Int. J. Sci. Technol. Res. 9 (2020), 3972-3975.
  9. S. Ragamayi, Y. Bhargavi, C. Krishnaveni, P. Bindu, Lattice-Fuzzy Prime-Ideal of a Gamma-Near Ring, J. Crit. Rev. 7 (2020), 1–5. http://dx.doi.org/10.31838/jcr.07.13.01.
  10. B. Satyanarayana, Contributions to Near-Rings Theory, Doctoral Thesis, Nagarjuna University, 1984.
  11. P.K. Sharma, On Intuitionistic Fuzzy Magnified Translation in Groups, Int. J. Math. Sci. Appl. 2 (2012), 139–146.
  12. N. Udten, N. Songseang, A. Iampan, Translation and Density of a Bipolar-Valued Fuzzy Set in UP-Algebras, Italian J. Pure Appl. Math. 41 (2019), 469–496.
  13. V.P.V. Korada, S. Ragamayi, Application of Bi-Polar Fuzzy Theory to Ideals in Gamma-near Rings and It’s Characteristics, AIP Conf. Proc. 2707 (2023), 020015. https://doi.org/10.1063/5.0143352.
  14. V.P.V. Korada, S. Ragamayi, G. Jayalalitha, Some Results on Bi-Polar Fuzzy Bi-Ideals of Γ-near Rings, in: Jakarta, Indonesia, AIP Conf. Proc. 2707 (2023), 020014. https://doi.org/10.1063/5.0143353.
  15. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
  16. W.R. Zhang, Bipolar Fuzzy Sets and Relations: A Computational Framework for Cognitive Modeling and Multiagent Decision Analysis, in: Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, IEEE, San Antonio, TX, USA, 1994: pp. 305–309. https://doi.org/10.1109/IJCF.1994.375115.