Fuzzy information systems and their homomorphisms

With the arrival of the information age, information acquisition and communication have become more and more important in the field of information technology. This paper uses the concept of homomorphism as a basic tool to study the communication between fuzzy information systems. The concepts of consistent and compatible mappings with respect to fuzzy sets are firstly defined and their basic properties are studied. Then, a pair of lower and upper rough fuzzy approximation operators is constructed by means of the concept of fuzzy mappings. Basic invariant properties of the approximation operators are investigated. Finally, the concepts of fuzzy information system and its homomorphism are introduced, and some invariant properties of fuzzy information systems under homomorphisms are examined. It is proved that the attribute reductions of an original information system and its image system are equivalent to each other in the context of fuzzy attributes. These results may have potential applications in attribute reduction and classification issues.