Structural Analysis of Two‐Fold Algebraic Systems Defined Over Fuzzy and Antifuzzy Groups

This study examines the structural properties of two‐fold algebras defined over fuzzy groups and antifuzzy groups. The corresponding two‐fold binary operations are introduced, and their fundamental algebraic features, such as associativity, identity elements, inverses, and finite order elements, are analyzed. In addition, several related substructures, including two‐fold subalgebras, centers, normality conditions, and homomorphisms, are described and their relationships with the underlying groups are discussed. Illustrative examples are included to demonstrate the developed framework. The findings contribute to the theory of fuzzy algebraic systems and indicate possible applications in modeling uncertainty and multivalued logical systems.