Generalized bipolar fuzzy GK-subalgebras and ideals in GK-algebras

In this paper, we introduce and study generalized bipolar fuzzy GK-subalgebras and GK-ideals in GK-algebras. Several fundamental properties of these structures are established with the help of suitable examples. We investigate their relationships with level subalgebras and level ideals and characterize these structures through their corresponding level sets. We also examine the relationship between generalized bipolar fuzzy GK-subalgebra and the usual bipolar fuzzy GK-subalgebras, as well as between generalized bipolar fuzzy GK-ideals and the usual bipolar fuzzy GK-ideals. Examples are provided to illustrate that these structures do not always coincide. Finally, we introduce a further generalized class of bipolar fuzzy GK-ideals and investigate some of its fundamental properties. These results contribute to the development of bipolar fuzzy structures within the framework of GK-algebras.