This work demonstrates connections between intuitionistic fuzzy WSBG-ideals and Sheffer stroke BG-algebras, suggesting novel reasoning methods under uncertainty.
In this paper, we investigate intuitionistic fuzzy WSBG-ideals and intuitionistic fuzzy implicative WSBG-ideals within the framework of Sheffer stroke BG-algebras. We establish new algebraic structures that extend classical Boolean and BG-algebra frameworks by synthesizing intuitionistic fuzzy set theory, introduced by Atanassov, with the Sheffer stroke operation. We demonstrate a fundamental connection between intuitionistic fuzzy implicative WSBG-ideals and their level sets, showing that the level set of an intuitionistic fuzzy implicative WSBG-ideal corresponds to an implicative WSBG-ideal of the Sheffer stroke BG-algebra. Furthermore, we explore the properties of intuitionistic fuzzy WSBG-ideals, proving that every intuitionistic fuzzy implicative WSBG-ideal is also an intuitionistic fuzzy WSBG-ideal. However, the converse does not always hold. This work provides new insights into the algebraic properties of Sheffer stroke BG-algebras, enabling novel reasoning methods under uncertainty and paving the way for further applications in fuzzy logic and computational models.
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Öner et al. (2025) studied this question.
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