Characterization of Bipolar Fuzzy SBG-Ideals in Sheffer Stroke BG-Algebras
Articles > Article · 2025
Authors: Neelamegarajan Rajesh, Tahsin ÖNER, İbrahim ŞENTÜRK, Kannan Geetha
Journal of Basic & Applied Sciences, Refereed Journals of Other Institutions, International, Index Copernicus e-Journals Database, 2025, vol 21, pp 149-158
DOI: 10.29169/1927-5129.2025.21.16
Summary
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.