Pythagorean fuzzy LiuB – subalgebra of LiuB - algebra

Background This article introduces the fuzzy Liu B -subalgebra (LBS) of Liu B -algebra (LBA), a concept previously undefined in the context of BCL-algebras (other than BCL + -algebras). Additionally, we explore the use of a new notion of Pythagorean fuzzy sets within Liu B -subalgebras of Liu B -algebra. Methods We define the Pythagorean fuzzy Liu B -subalgebra and investigate its basic characteristics. The methodology involves applying the concept of Pythagorean fuzzy sets to Liu B -subalgebras, with a focus on properties such as the complement of a fuzzy set, square deviation, accuracy function, score function, and degree of indeterminacy. Results The paper introduces a new concept—the Pythagorean fuzzy Liu B -subalgebra of Liu B -algebra—and provides theorems and properties associated with this structure. These findings demonstrate how these fuzzy subalgebras can be defined and explored within the broader framework of Liu B -algebra. Conclusions This work contributes to the theory of Liu B -algebras by presenting the Pythagorean fuzzy Liu B -subalgebra, along with its key properties and characteristics. The study provides new insights into the relationships between fuzzy sets and Liu B -algebras, opening up further avenues for research in this area.