Further Investigation of Characteristic Relation in Incomplete Information System

In the recent years, the method to expand Pawlak's rough set model in different kinds of information systems has become a hot topic. This article presents explorative research focusing on the transition from the traditional information system to a complex system—the incomplete information system. In such information system, “do not care” and lost unknown attribute values coexist. With a further investigation of Grzymala-Busse's characteristic relation in the incomplete information system, two unreasonable situations in the analysis of the classified problem are presented. To conduct sound classification in the incomplete information system, a new characteristic relation is proposed and by use of this new characteristic relation, the complete covering on the universe is formed. Based on the maximal complete compatible classes in the complete covering, two notions of the knowledge representation system are presented and some important properties associated with these knowledge representation systems are discussed. For further illustration, an example is analyzed. The research is meaningful both in theory and in applications for the extension of the rough set theory in incomplete information systems.