Attribute reduction with homomorphism in incomplete information systems

The notion of homomorphism is used as a tool to deal with attribute reduction in incomplete information systems. In this paper, we define a tolerance relation on the universe of discoures U, and the tolerance classes which are created by the tolerance relation can form a cover of U. Then a novel definition of consistent function is proposed, and some properties of incomplete information systems under homomorphism are discussed. Furthermore, we prove that the attribute reduction of the original system and its image system is equivalent to each other. And then a new and more convenient measure to handle the attribute reduction of the original incomplete information system is obtained.