Attribute Reduction in Bipolar Intuitionistic Fuzzy Relation System

Bipolar intuitionistic fuzzy relation system (BIFRS) effectively characterize the bipolarity in real-world data by introducing positive and negative membership and non-membership degrees. To address redundancy caused by high-dimensional attributes, this paper proposes an attribute reduction method based on bipolar intuitionistic discernibility matrices. By constructing positive discernibility matrix M+∗ matrix M−∗ and negative discernibility , we systematically identify the minimal attribute subset that satisfies the bipolar consistency condition h = + O=h− h− , where O⊆Q h+ and are discernibility functions derived from their disjunctive normal forms. Theoretical proofs demonstrate that the global relation SQ relation SO N P N P (π ,π ,η ,η ) and reduced maintain complete consistency across all four components if and only if O covers all positive and negative discernibility terms. Furthermore, we develop an efficient reduction algorithm that reduces time complexity through optimized matrix operations. Experimental results on real-world datasets validate the algorithm's effectiveness and superiority. This work not only extends the reduction theories of traditional fuzzy sets and rough sets, but also provides interpretable and efficient tools for decision support and feature selection applications.