Filters of Sheffer Stroke BL-Algebras Associated With a New Type of Fuzzy Set and Fuzzy Points

Ahn, Sun Shin; Seo, Young Joo; Jun, Young Bae

doi:10.28924/2291-8639-23-2025-167

Research Article

Filters of Sheffer Stroke BL-Algebras Associated With a New Type of Fuzzy Set and Fuzzy Points

Sun Shin Ahn*
Young Joo Seo
Young Bae Jun

* Corresponding author

Abstract

(Ultra) filters in Sheffer stroke BL-algebras based on the Jun’s J^δ_Y-fuzzy set are studied. The concept of (ultra) (∈, ∈)-J^δ_Y-fuzzy filters in Sheffer stroke BL-algebras is introduced, and various fundamental properties are investigated. Characterizations of (∈, ∈)-J^δ_Y-fuzzy filters are discussed, and the relationship between the fuzzy filter and the (∈, ∈)-J^δ_Y-fuzzy filter is considered. The conditions for the (∈, ∈)-J^δ_Y-fuzzy filter to become ultra are explored.

How to Cite

S. S. Ahn, Y. J. Seo, Y. B. Jun, Filters of Sheffer Stroke BL-Algebras Associated With a New Type of Fuzzy Set and Fuzzy Points, Int. J. Anal. Appl. 23 (2025), 167. https://doi.org/10.28924/2291-8639-23-2025-167

BibTeX

@article{Ahn2025,
  author  = {Ahn, Sun Shin and Seo, Young Joo and Jun, Young Bae},
  title   = {Filters of Sheffer Stroke BL-Algebras Associated With a New Type of Fuzzy Set and Fuzzy Points},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {167},
  doi     = {10.28924/2291-8639-23-2025-167}
}

References

[1] M. Anbarloei, Interval Valued (α, β)-Fuzzy Hyperideals in Krasner (m, N)-Hyperrings, J. Algebr. Hyperstruct. Log. Algebr. 4 (2023), 13–25. https://doi.org/10.61838/kman.jahla.4.1.2.
[2] I. Chajda, R. Halaš, H. Länger, Operations and Structures Derived From Non-Associative MV-Algebras, Soft Comput. 23 (2018), 3935–3944. https://doi.org/10.1007/s00500-018-3309-4.
[3] Y. Jun, Positive Implicative Be-Filters of BE-Algebras Based on Lukasiewicz Fuzzy Sets, J. Algebr. Hyperstruct. Log. Algebr. 4 (2023), 1–11. https://doi.org/10.61838/kman.jahla.4.1.1.
[4] Y. Jun, A New Form of Fuzzy Set and Its Application in BCK-Algebras and BCI-Algebras, Ann. Fuzzy Math. Inf. 26 (2023), 165–175. https://doi.org/10.30948/afmi.2023.26.2.165.
[5] Y. Jun, E. Yang, E. Hwan Roh, Quasi-Subalgebras of Sheffer Stroke BL-Algebras Associated with Fuzzy Points and a New Type of Fuzzy Set, J. Algebr. Hyperstruct. Log. Algebr. 5 (2024), 19–32. https://doi.org/10.61838/kman.jahla.5.2.3.
[6] T. Oner, T. Katican, A. Borumand Saeid, On Sheffer Stroke Be-Algebras, Discuss. Math. - Gen. Algebr. Appl. 42 (2022), 293–314. https://doi.org/10.7151/dmgaa.1391.
[7] T. Katican, T. Oner, A. Borumand Saeid, Stabilizers on Sheffer Stroke BL-Algebras, Honam Math. J. 44 (2022), 78–97. https://doi.org/10.5831/HMJ.2022.44.1.78.
[8] T. Katican, T. Oner, A. Rezaei, F. Smarandache, Neutrosophic -Structures Applied to Sheffer Stroke Bl-Algebras, Comput. Model. Eng. Sci. 129 (2021), 355–372. https://doi.org/10.32604/cmes.2021.016996.
[9] S. Mirvakili, H. Naraghi, M. Shirvani, Connections Between Fuzzy Multi-Groups and Fuzzy Multi-Graphs, J. Algebr. Hyperstruct. Log. Algebr. 2 (2021), 47–60. https://doi.org/10.52547/hatef.jahla.2.2.47.
[10] S. Mirvakili, H. Naraghi, M. Dehghanizadeh, H. Naraghi, On the Equivalence of Sequences Dependent on Fuzzy Ideals in the Bci-Algebra, J. Algebr. Hyperstruct. Log. Algebr. 3 (2022), 65–73. https://doi.org/10.52547/hatef.jahla.3.4.5.
[11] A. Namdar, Fuzzy N-Fold Fantastic Filters on Hoop Algebras, J. Algebr. Hyperstruct. Log. Algebr. 4 (2023), 189–203. https://doi.org/10.61838/kman.jahla.4.2.12.
[12] T. Oner, T. Katican, A. Borumand Saeid, (Fuzzy) Filters of Sheffer Stroke BL-Algebras, Kragujev. J. Math. 47 (2023), 39–55. https://doi.org/10.46793/kgjmat2301.039o.
[13] T. Oner, T. Kalkan, A.B. Saeid, Class of Sheffer Stroke Bck-Algebras, An. Univ. "Ovidius" Constanta - Ser. Mat. 30 (2022), 247–269. https://doi.org/10.2478/auom-2022-0014.
[14] T. Oner, T. Kalkan, A. Borumand Saeid, (Anti) Fuzzy Ideals of Sheffer Stroke BCK-Algebras, J. Algebr. Syst. 11 (2023), 105–135. https://doi.org/10.22044/jas.2022.11512.1582.
[15] T. Oner, I. Senturk, The Sheffer Stroke Operation Reducts of Basic Algebras, Open Math. 15 (2017), 926–935. https://doi.org/10.1515/math-2017-0075.
[16] P. Pao-Ming, L. Ying-Ming, Fuzzy Topology. I. Neighborhood Structure of a Fuzzy Point and Moore-Smith Convergence, J. Math. Anal. Appl. 76 (1980), 571–599. https://doi.org/10.1016/0022-247x(80)90048-7.
[17] G. Rezaei, Y. Jun, Commutative Ideals of BCI-Algebras Based on Łukasiewicz Fuzzy Sets, J. Algebr. Hyperstructures Log. Algebr. 3 (2022), 25–36. https://doi.org/10.52547/hatef.jahla.3.4.2.
[18] E.H. Roh, E. Yang, Y.B. Jun, Ideals of Bck-Algebras and Bci-Algebras Based on a New Form of Fuzzy Set, Eur. J. Pure Appl. Math. 16 (2023), 2009–2024. https://doi.org/10.29020/nybg.ejpam.v16i4.4933.
[19] I. Senturk, A View on State Operators in Sheffer Stroke Basic Algebras, Soft Comput. 25 (2021), 11471–11484. https://doi.org/10.1007/s00500-021-06059-8.
[20] H.M. Sheffer, A Set of Five Independent Postulates for Boolean Algebras, Trans. Amer. Math. Soc. 14 (1913), 481–488.
[21] X. Xin, F. Xiao, X. Yang, L-fuzzy Algebraic Substructure, J. Algebr. Hyperstruct. Log. Algebr. 4 (2023), 17–35. https://doi.org/10.61838/kman.jahla.4.2.2.
[22] L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.