Pythagorean Fuzzy Soft Structures on Boolean Rings

This paper introduces the concept of Pythagorean fuzzy soft (PFS) structures within the framework of Boolean rings (BRs), combining the expressive power of soft set theory and Pythagorean fuzzy sets in algebraic systems. We begin by defining fundamental operations on PFSSs—such as intersection, union, AND, and OR—and then specialize these structures to form Pythagorean fuzzy soft Boolean rings (PFSBRs). We further define Pythagorean fuzzy soft ideals (PFSIs) as a refined subclass of PFSBRs that exhibit ideal-like properties under the operations of the ring. Several theorems are established to demonstrate closure properties under these operations, with examples provided to illustrate the applicability and consistency of the proposed framework. This approach enhances the modeling of uncertainty in algebraic contexts and offers potential for future applications in decision science and soft computing.