Abstract: Attribute reduction is the fundamental approach of rough set theory to implement data mining, and its relevant algorithms are mainly based on the core. For the core, both its representation of the discernibility matrix and its calculation for finding the core exhibit important significance, but the existing discernibility matrix and its core algorithm have time and space limitations. According to the sparsity and large scale of the discernibility matrix, the block discernibility matrix based on the decision classification and its algorithm finding the core are proposed, and thus the decision classification information is directly applied to the form structure and problem solving. At first, the block discernibility matrix is defined by the decision classification, and its calculation algorithm is achieved. Then, based on the block discernibility matrix, the essence and algorithm of the core are provided. Finally, the proposed methods effectiveness is verified by the example and experiment. The block discernibility matrix based on the decision classification effectively implements the information extraction and dimensionality reduction, so its relevant algorithm finding the core well decreases the time and space complexities of the corresponding algorithm based on the discernibility matrix.

Key words: attribute reduction, core, block discernibility matrix, decision classification, discernibility matrix, rough set