Characteristic Relations in Generalized Incomplete Information System

In spite the fact that compatibility relation and similarity relation consider ´do not care´ data as lost data, they were introduced to rough set to deal with incomplete information system. Incomplete information system in which ´do not care´ data coexists with lost data, this article studies characteristic relation and discusses the unreasonable state which may be brought forth by characteristic class. On one hand, the two objects which do not have the same known value on a certain character seemed to be indiscernible. On the other hand, the two objects which have a lot of equivalent known values are very likely to be distinguished. In order to solve the problems of the classification in generalized incomplete information system, new kinds of characteristic relations named as I and II are brought forth and characteristic relation III is also constructed on advantages of characteristic relation I and II, and at last the validity of the newly constructed characteristic relations is also demonstrated with examples.