Bipolar Fuzzy Filters of Gamma-Near Rings

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-2
Published: Jan 3, 2024
Cite as:
V. P. Vineela Korada, S. Ragamayi, Aiyared Iampan, Bipolar Fuzzy Filters of Gamma-Near Rings, Int. J. Anal. Appl., 22 (2024), 2.

Main Article Content

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

Abstract

The main objective of this paper is to present the notation of bipolar fuzzy filters of Γ-near rings and ordered Γ-near rings. As a consequence, we deal with bipolar fuzzy prime ideals of Γ-near rings and ordered Γ-near rings. Also, we examine the one-to-one correspondence of bipolar fuzzy filters and crisp filters of Γ-near rings. Later, we define and study the homomorphism of ordered Γ-near rings.

Article Details

References

  1. G.L. Booth, A Note on Γ-Near Rings, Stud. Sci. Math. Hung. 23 (1988), 471–475.
  2. Y.B. Jun, M. Sapanci, M.A. Öztürk, Fuzzy Ideals in Gamma Near-Rings, Turk. J. Math. 22 (1998), 449–549.
  3. K.J. Lee, Bipolar Fuzzy Subalgebras and Bipolar Fuzzy Ideals of BCK/BCI-Algebras, Bull. Malays. Math. Sci. Soc. 32 (2009), 361–373.
  4. N. Meenakumari, T.T. Chelvam, Fuzzy Bi-Ideals in Gamma Near-Rings, J. Algebra Discr. Struct. 9 (2011), 43–52.
  5. N. Nobusawa, On a Generalization of the Ring Theory, Osaka J.Math. 1 (1964), 81–89. https://doi.org/10.18910/12354.
  6. G. Pilz, Near-Rings: The Theory and Its Applications, North-Holland, Amsterdam, (1983).
  7. S. Ragamayi, Y. Bhargavi, A Study of Vague Gamma-Nearrings, 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-Nearring, J. Crit. Rev. 7 (2020), 1–5. https://doi.org/10.31838/jcr.07.13.01.
  10. S. Ragamayi, G. Jaya Lalitha, P. Bindu, On L-Vague Maximal-Ideal of a Γ-Near Ring, AIP Conf. Proc. 2375 (2021), 020017. https://doi.org/10.1063/5.0066395.
  11. S. Ragamayi, N. Konda Reddy, P. Bindu, On L-Vague Prime-Ideal of a Γ-Near Ring and Its Characteristic Properties, AIP Conf. Proc., 2375, (2021), 020020. https://doi.org/10.1063/5.0066396.
  12. S. Ragamayi, N. Konda Reddy, G.J. Lalitha, P. Bindu, A Study of L-Fuzzy Cosets of a Γ-Near Ring, AIP Conf. Proc., 2375, (2021), 020010. https://doi.org/10.1063/5.0066393
  13. S. Ragamayi, N. Konda Reddy, B.S. Kumar, Results on L-Vague Ideal of a Γ-Near Ring, AIP Conf. Proc. 2375 (2021), 020014. https://doi.org/10.1063/5.0066388.
  14. M.M.K. Rao, Fuzzy Filters in Ordered Γ-Semirings, Caspian J. Math. Sci. 8 (2019), 18–34. https://doi.org/10.22080/cjms.2018.12048.1314.
  15. M.M.K. Rao, B. Venkateswarlu, Fuzzy Filters in Γ-Semirings, Malaya J. Mat. 3 (2015), 93–98. https://doi.org/10.26637/mjm301/009.
  16. B. Satyanarayana, Contributions to Near-Rings Theory, Doctoral Thesis, Nagarjuna University, (1984).
  17. 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.
  18. V.P.V. Korada, S. Ragamayi, G.J. Lalitha, Some Results on Bi-Polar Fuzzy Bi-Ideals of Γ-Near Rings, AIP Conf. Proc. 2707 (2023), 020014. https://doi.org/10.1063/5.0143353.
  19. L.A. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  20. 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.