T-Fuzzy Structure on JU-Algebra.

Introduction: This study explored the application of T-norms in fuzzy algebra, specifically by examining JU-subalgebras and JU-ideals derived from crisp JU-algebras. We investigated the properties of the T-fuzzy structures within this algebraic framework. Our work focuses on characterizing idempotent T-fuzzy JU algebras and analyzing their behavior in Cartesian products. Method: We begin by defining T-fuzzy JU-subalgebras and JU-ideals using T-norm operations. Next, we examine the structural properties of these algebraic systems through a theoretical analysis. We then studied the idempotent cases to identify their distinctive features. Finally, we prove the closure properties by constructing Cartesian products of these fuzzy structures. Conclusion: Our analysis demonstrated that idempotent T-fuzzy JU algebras possess unique structural characteristics. Furthermore, we establish that the Cartesian product of the two T-fuzzy JU-subalgebras remains a T-fuzzy JU-subalgebra, and similarly for JU-ideals. These findings extend the theoretical foundations of fuzzy algebra and suggest its potential applications in related mathematical fields.