Abstract: In order to deal with the incomplete,symbol and numeric hybrid data directly,a new kind of generalized neighborhood relationship was constructed by combining with relative neighborhood relationship and tolerance relationship．Under the general neighborhood relationship,the conditional entropy used for incomplete hybrid decision system was defined on the basis of information entropy．It was proved that the attibute significance of the condition entropy contains that of the positive regions in this paper．And then the reduction algorithm based on conditional entropy of incomplete hybrid decision system was constructed．The experiments on six hybrid attribute UCI datasets were made,and the proposed method and the similar methods were compared in aspects of feature gene number,classification accuracy and run-time.The results show that the method of feature gene selection based on the proposed extended rough set model is effective.

Key words: Incomplete hybrid decision system,Generalized neighborhood relation,Rough set,Conditional entropy