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Since fuzzy β -covering was proposed, few papers have focused on how to calculate the reduct in fuzzy β -covering and how to update the reduct while adding and deleting some objects of the universe. Here, we propose a matrix-based approach for computing the reduct in a fuzzy β -covering and updating it dynamically using a matrix. First, matrix forms for computing the reduct in a fuzzy β -covering are proposed. Second, properties of the matrix-based approaches are studied while adding and deleting objects. Then, matrix-based algorithms for updating the reduct in a fuzzy β -covering are proposed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.

Updating the Reduct in Fuzzy β-Covering via Matrix Approaches While Adding and Deleting Some Objects of the Universe