\((\in, \in \vee q_{k})\)-Intuitionistic Fuzzy Soft Boolean Near-Rings

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-91
Published: Apr 14, 2025
Cite as:
Gadde Sambasiva Rao, D. Ramesh, Aiyared Iampan, G. Vijaya Lakshmi, B. Satyanarayana, \((\in, \in \vee q_{k})\)-Intuitionistic Fuzzy Soft Boolean Near-Rings, Int. J. Anal. Appl., 23 (2025), 91.

Main Article Content

Gadde Sambasiva Rao, D. Ramesh, Aiyared Iampan, G. Vijaya Lakshmi, B. Satyanarayana

Abstract

This study proposes an enriched algebraic framework through the introduction of (∈, ∈ ∨qk)-intuitionistic fuzzy soft Boolean near-rings (IFSBNs), a class of mathematical structures that generalize previous fuzzy and soft ideal systems within Boolean near-rings. Building upon established theories, we define the corresponding (∈, ∈ ∨qk)- intuitionistic fuzzy soft ideals (IFSIs) and idealistic forms (IIFSBNs), and rigorously analyze their properties using formal definitions and examples. By expanding the capacity to model uncertainty and complex relationships, this work contributes to the theoretical backbone required for developing future intelligent systems. Importantly, the abstract nature of these algebraic tools makes them highly adaptable to curriculum designs in mathematics-focused educational environments, aligning with Sustainable Development Goal 4 (Quality Education). In particular, the framework can inspire high school and university students in research-intensive programs to engage in exploratory learning and abstract reasoning. Furthermore, this contribution exemplifies how collaborative academic efforts across institutions can produce foundational knowledge that transcends disciplinary boundaries, supporting SDG 17 (Partnerships for the Goals). The cross-institutional authorship and integration of interdisciplinary concepts promote educational equity and intellectual cooperation, fostering a culture of shared research innovation globally.

Article Details

References

  1. S. Abou-Zaid, On Fuzzy Subnear-Rings and Ideals, Fuzzy Sets Syst. 44 (1991), 139–146. https://doi.org/10.1016/0165-0114(91)90039-S.
  2. S.K. Bhakat, P. Das, (∈, ∈ ∨q)-Fuzzy Subgroup, Fuzzy Sets Syst. 80 (1996), 359-368. https://doi.org/10.1016/0165-0114(95)00157-3.
  3. P. Dheena, S. Coumaressane, Generalization of (∈, ∈ ∨q)-Fuzzy Subnear-Rings and Ideals, Iran. J. Fuzzy Syst. 5 (2008), 79-97. https://doi.org/10.22111/ijfs.2008.318.
  4. B.A. Ersoy, S. Onar, K. Hila, B. Davvaz, Some Properties of Intuitionistic Fuzzy Soft Rings, J. Math. 2013 (2013), 650480. https://doi.org/10.1155/2013/650480.
  5. P. Gunter, Near-Rings: The Theory and Its Applications, North-Holland, Amsterdam, 1983.
  6. E. Inan, M.A. Öztürk, Fuzzy Soft Rings and Fuzzy Soft Ideals, Neural Comput. Appl. 21 (2012), 1–8. https://doi.org/10.1007/s00521-011-0550-5.
  7. P.K. Maji, R. Biswas, A.R. Roy, Fuzzy Soft Sets, J. Fuzzy Math. 9 (2001), 589-602.
  8. P.K. Maji, R. Biswas, A.R. Roy, Intuitionistic Fuzzy Soft Sets, J. Fuzzy Math. 9 (2001), 677-692.
  9. P.K. Maji, R. Biswas, A.R. Roy, Soft Set Theory, Comput. Math. Appl. 45 (2003), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6.
  10. D. Molodtsov, Soft Set Theory—First Results, Comput. Math. Appl. 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5.
  11. Al. Narayanan, T. Manikantan, (∈, ∈ ∨q)-Fuzzy Subnear-Rings and (∈, ∈ ∨q)-Fuzzy Ideals of Near-Rings, J. Appl. Math. Comput. 18 (2005), 419–430. https://doi.org/10.1007/BF02936584.
  12. M.A. Öztürk, E. ˙Inan, Fuzzy Soft Subnear-Rings and (∈, ∈ ∨q)-Fuzzy Soft Subnear-Rings, Comput. Math. Appl. 63 (2012), 617–628. https://doi.org/10.1016/j.camwa.2011.11.008.
  13. S.R. Gadde, Pushpalatha. Kolluru, B.P. Munagala, A Note on Soft Boolean Near-Rings, AIP Conf. Proc. 2707 (2023), 020013. https://doi.org/10.1063/5.0148444.
  14. S.R. Gadde, P. Kolluru, N. Thandu, Soft Intersection Boolean Near-Rings with Its Applications, AIP Conf. Proc. 2707 (2023), 020012. https://doi.org/10.1063/5.0148443.
  15. G.S. Rao, K. Pushpalatha, Ramesh D., S.V.M. Sarma, G. Vijayalakshmi, A Study on Boolean like Algebras, AIP Conf. Proc. 2375 (2021), 020018. https://doi.org/10.1063/5.0066293.
  16. G.S. Rao, R. Dasari, A. Iampan, B. Satyanarayana, Fuzzy Soft Boolean Near-Rings and Idealistic Fuzzy Soft Boolean Near-Rings, ICIC Express Lett. 18 (2024), 677-684. https://doi.org/10.24507/icicel.18.07.677.
  17. G. Sambasiva Rao, D. Ramesh, A. Iampan, B. Satyanarayana, Fuzzy Soft Boolean Rings, Int. J. Anal. Appl. 21 (2023), 60. https://doi.org/10.28924/2291-8639-21-2023-60.
  18. G.S. Rao, D. Ramesh, B. Satyanarayana, (∈, ∈ ∨qk)-Fuzzy Soft Boolean Near Rings, Asia Pac. J. Math. 10 (2023), 50. https://doi.org/10.28924/APJM/10-50.
  19. B. Satyanarayana, D. Ramesh, Y.P. Kumar, Interval Valued Intuitionistic Fuzzy Homomorphism of BF-Algebras, Math. Theory Model. 3 (2013), 15-23.
  20. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.