The attribute reduction model based on Skowrons discernibility matrix is equivalent to attribute reduction model under algebra view. Its essence lies in preserving the discernible information between consistent objects and other objects, but cant describe the attribute reduction criterion of non-algebra view. The essence of attribute reduction criterion is to maintain a certain discernibility characteristic of decision information system, the decision information system has many different discernibility characteristics, and the single attribute reduction criterion only describe one of them. In order to describe different attribute reduction criterions using uniform discernibility matrix, the conception of decision vectors for condition equivalence classes were defined and decision vector discernibility matrix was constructed based on this conception, then the discernibility matrix and discernibility function satisfying different reduction criterion were designed respectively. The equivalence between different reduction criterions and corresponding discernibility matrix was strictly proved. The Reasoning proof and simulation example shows the feasibility and effectiveness of the proposed method.