AFuzzy Dual Ideals and Their Lattice Structure in Bck-Algebras

Abstract

In this paper, we investigate several structural properties of fuzzy dual ideals within the framework of BCK-algebras. This result provides a direct algebraic characterization that links duality with the classical notion of filtering in BCK-structures.

Furthermore, we examine prime anti-dual fuzzy ideals and show that any such fuzzy ideal satisfies a functional identity of the form

which reveals how prime anti-dual behavior interacts with meet and join operations.

Finally, we characterize fuzzy dual ideals through the identity

which offers a functional criterion for determining when a fuzzy set in X behaves as a fuzzy dual ideal. These results collectively deepen the understanding of fuzzy dual structures in BCK-algebras and provide new tools for analyzing their order-theoretic behavior.