Vol. 21 (2025), Mathematics
Vol. 21 (2025)

Characterization of Bipolar Fuzzy SBG-Ideals in Sheffer Stroke BG-Algebras

Mathematics
Published 2025-09-15
Neelamegarajan Rajesh
Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamilnadu, India
Tahsin Oner
Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey
Ibrahim Senturk
Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey
Kannan Geetha
Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamilnadu, India
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Keywords

SBG-algebras
Bipolar fuzzy sets
bipolar fuzzy SBG-ideals

How to Cite

Characterization of Bipolar Fuzzy SBG-Ideals in Sheffer Stroke BG-Algebras. (2025). Journal of Basic & Applied Sciences, 21, 149-158. https://doi.org/10.29169/1927-5129.2025.21.16
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Abstract

In this paper, we systematically develop the theory of bipolar-valued fuzzy sets in the setting of Sheffer stroke BG-algebras (SBG-algebras) by introducing and characterizing bipolar fuzzy SBG-subalgebras and SBG-ideals. Necessary and sufficient conditions for these structures are established via sss-cuts and ttt-cuts, along with explicit algorithms for their verification. We further investigate the relationship between bipolar-valued fuzzy sets and their crisp counterparts through constructive examples. It is shown that the intersection of bipolar fuzzy SBG-ideals preserves the ideal structure, and that the combination of the positive membership function with the complement of the negative membership function yields fuzzy SBG-ideals and subalgebras. These findings extend the algebraic framework of fuzzy logic and provide practical tools for modeling and analyzing bipolar uncertainty in algebraic systems.

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References

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