Extended results on the relationship between information systems

The relationship between information systems is an important topic in rough set field and it is studied through mappings. Many kinds of consistent functions have been proposed and they can be used to describe the invariance of attribute reducts between two information systems efficiently. However they cannot reflect relationships between neighborhoods generated from two information systems. In this paper, to achieve this aim, firstly, we introduce a neighborhood-continuous function that is inspired by the concept of continuous function in topology. Then, we address its properties and discuss relationships between neighborhood-continuous functions and several kinds of existing consistent functions. Furthermore, we investigate some important properties of neighborhood-continuous function with respect to relation mappings. Finally, based on neighborhood-continuous functions, the notion of a neighborhood-homomorphism between different information systems is proposed. It is noted that the reduct feature of a single information system can be described by neighborhood-continuous functions, while the reduct invariance of two different information systems can be described by neighborhood-homomorphisms.