An new algorithm of modifying hu's discernibility matrix and its attribute reduction

Hu's discernibility matrix is unsuitable for incompatibility decision table to compute core and attribute reduction and improved discernibility matrix need to add additional calculation. In order to avoid additional calculation while building discernibility matrix for both incompatibility decision table and compatibility decision table, a new algorithm of establishing discernibility matrix and attribute reduction is presented. Firstly, through analyzing traditional discernibility matrix, modified universe is put forward. And the modified discernibility matrix is got by using modified universe to modify Hu's matrix, avoiding additional calculation besides of matrix. Then, the properties of the core and attribute reduction are proposed and it is proved that the core and attribute reduction acquired from new matrix are equivalent to the core and attribute reduction based on positive region. The attribute reduction is provided at last and the example is used to explain the correctness of the method.