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There are many algorithms of attribute reduction based on discernibility matrix, where the element of the discernibility matrix is used as heuristic information. But there are few algebra methods about attribute reduction based on discernibility matrix. In this paper, we proposed an algorithm of attribute reduction with algebra method. First of all, we should design an algorithm to compute the heuristic information. Then we used this heuristic information to design an new algorithm of attribute reduction based on discernibility matrix, whose time complexity is O(|C| 2 |U|), and whose space complexity is O(|U|). At last, we used an example to illustrate the new algorithm's validity and high efficiency. So is attribute reduction algorithm of attribute reduction model based on information entropy proposed by Professor Wang, however, But the design of attribute reduction algorithm of discernibility matrix in algebraic method is less used, this is mainly because the model has no direct algebraic definition Reference (10-11) illustrates a new attribute reduction model based on information. Reference (12) has proved that the model is equal to the Attribute Reduction Algorithm Based on Discernibility Matrix. Of which Reference (13) has put forward a matrix method. So, the paper designs an algebra method of Attribute Reduction based on discernibility. The Specific steps are as follows: Firstly, we design a algorithm to calculate a heuristic information with rapid response, then based on the heuristic information we design Attribute Reduction algorithm based on discernibility matrix. Whose time complexity is O(|C| 2 |U|), and space complexity is O(|U|). At last, an example is provided to illustrate the new algorithm.

Attribute Reduction Algorithm Based on Discernibility Matrix with Algebraic Method