Bipolar Fuzzy Filters of Gamma-Near Rings

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

doi:10.28924/2291-8639-22-2024-2

Research Article

Bipolar Fuzzy Filters of Gamma-Near Rings

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

* Corresponding author

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.

How to Cite

V. P. Vineela Korada, S. Ragamayi, A. Iampan, Bipolar Fuzzy Filters of Gamma-Near Rings, Int. J. Anal. Appl. 22 (2024), 2. https://doi.org/10.28924/2291-8639-22-2024-2

BibTeX

@article{Korada2024,
  author  = {Vineela Korada, V. P. and Ragamayi, S. and Iampan, Aiyared},
  title   = {Bipolar Fuzzy Filters of Gamma-Near Rings},
  journal = {Int. J. Anal. Appl.},
  volume  = {22},
  year    = {2024},
  pages   = {2},
  doi     = {10.28924/2291-8639-22-2024-2}
}

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.