Bipolar fuzzy GE-algebras

This paper introduces the concept of a bipolar fuzzy GE-algebra within the framework of GE-algebras and explores its key properties. It offers a characterization of a bipolar fuzzy GE-algebra utilizing the negative ∈λ-set and the positive ∈α-set. Additionally, a criterion is provided for identifying a bipolar fuzzy set as a bipolar fuzzy GE-algebra. The paper defines negative qλ-sets and positive qα-sets of a bipolar fuzzy set, presenting necessary conditions for these sets to be GE-subalgebras of a GE-algebra. Furthermore, it introduces the notion of a bipolar (∈, ∈∨q )-fuzzy GE-algebra and investigates its properties, including necessary and sufficient conditions for a bipolar fuzzy set to qualify as such. Finally, the characterization of a bipolar (∈, ∈∨q )-fuzzy GE-algebra using the negative ∈λ-set and the positive ∈α-set is discussed