Abstract: In neighborhood system, by analyzing the inclusion and intersection between neighborhoods and target, two different types of neighborhood system based rough sets were presented, and two sets of properties for describing the monotonic verities of levels of neighborhood systems were proposed immediately. Moreover, two different quasi-orderings were also proposed to express the coarser or finer relationships between neighborhood systems. It is proven that there arc corresponding relationships between two quasi-ordering and two sets of properties, respectively.

Key words: Neighborhood system, Rough set , Neighborhood,Quasii-ordering