Abstract: As for a decision system with both missing attribute values and mixed data types,the classical rough sets theory cannot directly do anything about it.Such a decision system was firstly defined as the incomplete mixed decision system (IMDS).Secondly,the limited neighborhood relation was proposed for composing the attribute reduction algorithm of a novel incomplete mixed decision system for IMDS,which employed the conditional entropy as the heuristic factor to make up for the positive region of decision deficiency.Based on the limited neighborhood relation,the nominal attribute and the numerical attribute and the missing attribute could be handled simultaneously by the proposed reduction algorithm without the discretization of numerical attributes or completing the incomplete data.Finally,the proposed reduction algorithm was tested on several UCI data sets.The experiment results show that the reduction algorithm can select the core attributes on the condition of keeping or improving classification accuracy.Also,how to impact the classification when specifying the value of the threshold used in the limited neighborhood relation is specified also discussed.

Key words: incomplete mixed decision system, limited neighborhood relation, conditional entropy, attribute reduction