Approximation Partition Spaces of Covering Space

In incomplete, uncertain or fuzzy information processing, a universe could be divided into some subparts which might be a covering space of the original universe according to some dividing principle. Several researchers have proposed some covering space models for uncertain information processing. A covering space could be taken as a fuzzy knowledge space while a partition space as a crisp knowledge space. From the viewpoint of granular computing, fuzzy knowledge space and crisp knowledge space are different representation forms of knowledge on different granularity levels, and they could be transformed into each other by changing the knowledge granularity. In this paper, through adjusting the knowledge granularity of covering spaces, a method for transforming a covering spaceC into two boundary partition space is proposed. The relationship between a covering space and its two boundary partition spaces is analyzed. Some ideas for transforming a covering space into partition spaces and vise versa, and transforming a covering space into another covering space in different granularity degree, are also discussed.