Rough Intuitionistic Fuzzy Filters in BE-Algebras: Applications in Artificial Intelligence and Medical Diagnosis

This paper proposes a theoretical framework for studying rough intuitionistic fuzzy filters within the structure of BE-algebras. Building on rough set theory and intuitionistic fuzzy set theory, we introduce rough intuitionistic fuzzy filters via lower and upper approximation operators induced by congruence relations. To further generalize the framework, we define set-valued homomorphisms on BE-algebras and use them to formulate $\Gamma$-rough intuitionistic fuzzy filters. Several structural properties and characterization results are established, including stability under approximation operators, relationships with classical intuitionistic fuzzy filters, and preservation under homomorphic mappings. The proposed approach provides an algebraic mechanism for modeling uncertainty, hesitation, and imprecision in implication-based systems, with potential relevance to uncertainty-aware reasoning in artificial intelligence, decision-support systems, and medical diagnosis.