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This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation for the establishment of T-rough intuitionistic fuzzy ideals. The characterization of these innovative ideals is accomplished by employing the (α,β)-cut of intuitionistic fuzzy sets in the context of BCK-algebras.
Alsager et al. (Fri,) studied this question.