One of the most attentive applications of rough set is attribute reduction. Addressing the noise in decision information systems, a new method for importance measure of attribute set is presented from the point of view that knowledge can enhance the ability to perform classification. In addition, a new approximate attribute reduction algorithms is proposed based on general binary relation, which can be used to deal with noise and be applicable to many extending model of rough sets. Experimental results demonstrate that the proposed approximate attribute reduction algorithms can effectively increase sensitivity to noise, achieve more compact reduction, and simultaneously improve the classification performance.