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Tolerance relation, similarity relation and characteristic relation are discussed. Three types unknown attribute value of “missing value”, “lost value” and “any value” are discussed. Semantically, “missing value”, denoted by “*”, is the same as the unknown value in the tolerance relation, “lost value”, denoted by “?”, is the same as the unknown value in the similarity relation and the “lost value” in the characteristic relation, and “any value”, denoted by “#”, is same as “do not care” condition in characteristic relation. The difference of The definitions of new incomplete information system, attribute similarity and object similarity are given to process the incomplete information system with three types unknown attribute value. Base on these definitions, a new characteristic relation is proposed, characteristic class; lower approximation and upper approximation are defined for new characteristic relation.