Theoretical analysis on the relations between distance and close-degree based on granular computing

According to the granular computing approaches and the theories of soft computing, the axiomation definition of formula is given out. We define strictly the granular by the formulas in this artical. It presents an approach to describe and measure the difference and the similarity between the granularities the distance and close-degree of granular computing. And every definition is expressed by formula. This similarity measuring method is simple and effective. We discuss and prove the relationship of distance and close-degree of granular computing. These conclusions will be help people to understand granular properties. The research is helpful for guiding to establish the granule computing in an information system.