Abstract: Discernibility matrix expresses the distinguishing information of all objects in the information system with matrix elements,which provides a new idea for attribute reduction.However,the traditional discernibility matrix uses the core attributes to eliminate redundant element items after the construction is finished,ignoring the role of the core attributes in the matrix construction process.In response to this problem,the following research is done.Firstly,the definition of the discernibility matrix is optimized.Before calculating the distinguishing information of any two objects,it is first determined whether the values on the core attributes are equal.If not,the corresponding element items are directly recorded as ø,and the judgment of other attributes is ignored.Secondly,the concept of attribute weighted importance is proposed.The ratio of each condition attribute to the non-empty element term in the discernibility matrix (called macro importance) and the contribution of each attribute to the distinguishing object (called micro Importance) are comprehensively considered,and the rationality of the measurement method is illustrated by an example.Thirdly,aiming at the disadvantages that there are a lot of redundant elements and empty sets in the optimized discernibility matrix,by combining the concept of discernibility information tree,discernibility information tree based on optimized discernibility matrix and attribute weighted importance is proposed.All non-empty element items in the optimized discernibility matrix are sorted according to attribute weighted importance,so that attributes with high importance are shared by more nodes.Element items that do not contain core attributes are mapped to a path in the tree during the build process,while element items that contain core attributes are ignored.Finally,a reduction algorithm HSDI-tree based on optimized discernibility matrix and improving discernibility information tree is proposed.This paper compared the reduction results and the number of nodes of the HSDI-tree algorithm,CDI-tree,DI-tree and IDI-tree algorithms on the five data sets of UCI.The experimental results show that the HSDI-tree algorithm can effectively find the minimum attribute reduction and has better space compression ability.

Key words: Attribute importance, Attribute reduction, Discernibility information tree, Discernibility matrix, Rough set