Some Algebraic Properties of Pythagorean Fuzzy Bi-ideals

Fuzzy sets have a significant place in solving problems involving uncertainty. There are many studies on fuzzy sets in decision-making, engineering, algebra, etc. In this study, we discuss the behavior of Pythagorean fuzzy sets, which are a kind of generalization of fuzzy sets in algebra. First, we define the Pythagorean fuzzy product and examine some of its properties. Then, we investigate the relationship between the Pythagorean fuzzy ideal and the Pythagorean fuzzy product. Then, we define Pythagorean fuzzy bi-ideal. We give the theorem that characterizes bi-ideals in terms of fuzzy bi-ideals. We examine the behavior of Pythagorean fuzzy bi-ideals under Pythagorean fuzzy product. We prove that the intersection, Cartesian product, and Pythagorean fuzzy product of Pythagorean fuzzy bi-ideals are also Pythagorean fuzzy bi-ideals. Furthermore, we investigate the image and the inverse image of the Pythagorean fuzzy bi-ideal.