<p>In the real world, there is a significant amount of incomplete data, making attribute reduction for incomplete data a critical issue. Many existing reduction methods mainly study the relationship between conditional attributes and decision attributes, and often lack the correlation between conditional attributes. In this paper, first, incomplete Euclidean distance and global similarity are proposed, and correspondingly, fused fuzzy similarity relations are constructed to characterize the fuzzy similarity relations between objects with missing values, and to generate an object relation matrix. Second, incomplete cosine similarity is proposed to characterize the similarity between conditional attributes, and an attribute relation matrix is generated to describe the correlation between conditional attributes. Finally, we construct the bidirectional fuzzy similarity discriminability (BFD) and the corresponding reduction algorithm on this basis. Under the KNN classifier, the average lead compared to other state-of-the-art algorithms is 6.44%, and this value reaches 6.67% under the CART classifier and demonstrate the effectiveness of the algorithm through experiments.</p>