Extension of Rough Set Theory Based on Strict Similarity Relation

From researching tolerance relation and valued tolerance relation, we draw a conclusion that the “similarity” of two objects in incomplete information systems defined by tolerance relation and having missing attribute values is very low. We introduce a new extension of rough set based on strict similarity relation, in which the missing values are considered as “any value”, denoted by *. We regard * as a specific attribute value, two * values are equal, * is not equal to any other attribute values. By strict similarity relation we convert incomplete information systems to complete information systems, the new extension not only overcomes the shortcomings of tolerance relation, but also makes classical rough set theory can be directly used to deal with incomplete information systems.