Pythagorean fuzzy LiuB – subalgebra of LiuB - algebra

Background This article introduces the fuzzy LiuB-subalgebra (LBS) of LiuB-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 LiuB-subalgebras of LiuB-algebra. Methods We define the Pythagorean fuzzy LiuB-subalgebra and investigate its basic characteristics. The methodology involves applying the concept of Pythagorean fuzzy sets to LiuB-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 LiuB-subalgebra of LiuB-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 LiuB-algebra. Conclusions This work contributes to the theory of LiuB-algebras by presenting the Pythagorean fuzzy LiuB-subalgebra, along with its key properties and characteristics. The study provides new insights into the relationships between fuzzy sets and LiuB-algebras, opening up further avenues for research in this area.