Structural Analysis of Intuitionistic Fuzzy Implicative WSBG-Ideals
Makaleler > Tam Makale · 2025
Yazarlar: Tahsin ÖNER, Aiyared Iampan, Neelamegarajan Rajesh, İbrahim ŞENTÜRK
European Journal of Pure and Applied Mathematics, ESCI İndekslerine Giren Dergi, Uluslararası, Emerging Sources Citation Index (ESCI), 2025, cilt 18, ss 1-33
DOI: 10.29020/nybg.ejpam.v18i3.5894
Özet
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.