Decision table decomposition using core attributes partition for attribute reduction

The attribute reduction algorithms of decision table based on discernability matrix are required to construct discernability matrix, which reduces efficiency of algorithms. In this paper, a decision table decomposition model is proposed to solve the attribute reduction problem based on discernibility matrix for large decision table. By introducing the core attributes partition, the large decision table is divided into a number of decision sub-tables, which translates computing discernibility matrix in original decision table into computing discernibility matrix in decision sub-tables. The relationships between all the minimum attribute reductions of original decision table and all the attribution reductions of its decision sub-tables are first established. Based on the idea, a complete algorithm is presented, and all the minimum attribute reductions in the original decision table can be obtained from attribute reduction in its decision sub-tables. Theoretical analysis and numerical example results indicate that the algorithm can more easily explore all the minimum attribute reductions, and it is efficient.