A Unified Definition of Consistent Functions

In recent years, homomorphisms have been exploited to compare the structures and properties of two generalized information systems. Some of these homomorphisms are based on consistent functions, which are a class of special mappings between universal sets. The purpose of this paper is to unify and extend the consistent functions in the literature into the framework of neighborhood systems. After introducing the notion of consistent functions with respect to neighborhood systems, we explore some important properties of the extended consistent functions such as preserving the inverse images and the intersections of neighborhoods. Our results provide a sound basis for further investigating neighborhood systems via homomorphisms.