On bipolar fuzzy implicative ideals in Sheffer stroke BG-algebras

Abstract

This paper presents a comprehensive investigation into the algebraic integration of bipolar fuzzy logic and Sheffer stroke BG-algebras, introducing the concept of bipolar fuzzy Sheffer stroke BG-algebras. By embedding bipolar fuzzy sets—distinguished by their dual positive and negative membership degrees—into the Sheffer stroke BG-algebraic framework, we systematically examine the structure and properties of bipolar fuzzy subalgebras and various classes of SBG-ideals. Central to our approach is the analysis of level sets associated with bipolar fuzzy subsets, through which we establish rigorous correspondences between these fuzzy constructs and classical subalgebras and ideals. Our results reveal that the level sets of bipolar fuzzy SBG-subalgebras and SBG-ideals naturally inherit the underlying algebraic structure, subject to well-defined conditions. This theoretical advancement not only enhances the algebraic modeling of systems characterized by uncertainty and duality but also lays a solid foundation for further applications in logical inference, information processing, and computational intelligence within bipolar fuzzy contexts.