Properties Of Ordered Information Systems Under Homomorphisms

Information systems and rough sets theory are closely related in the practice application. Information systems are the basic tool for knowledge expression in rough sets theory. With the development of science and technology, information systems are used more and more widely in many fields, such as machine learning, information exchange and relational database field of artificial intelligence. This has brought a lot of new topics. In this paper, consistent function is viewed as a basic tool to research communication between ordered information systems. Properties of ordered information systems under mappings are investigated. In this paper, the main listed as follows:1. The concept of a consistent function related to a dominance relation is defined. We discuss the invariant properties of dominance relation mappings under the condition of consistent functions.2. The concept of ordered information systems and homomorphism of information systems are defined. We research their basic properties and discuss the relationship between ordered information systems and their image systems.3. The concept of ordered decision systems is defined. We discuss the properties of consistent ordered decision systems and inconsistent ordered decision systems. It is proved that attribute reductions in the original ordered systems(information systems and decision systems) and their image systems are equivalent to each other under the condition of homomorphisms.