Set-based Granular Computing: A Sphere Model

As an effective method to deal with information and knowledge processing, granular computing has recently received more attention from researchers. The foundations of granular computing involve general principles of many disciplines including divide and conquer, interval computing, fuzzy sets, and rough sets, which have been explored for many years. By introducing a so-called knowledge distance, this project aims to consistently represent knowledge in a sphere model. Under this uniform framework, we will investigate how to measure the information granularity of a granular space and develop an axiomatic definition of information granularity. Furthermore, we will propose four new operators on the sphere model and demonstrate these operators to be adequate for generating new knowledge from known knowledge. The expected outcomes of this project will be very helpful for revealing the essence of knowledge granulation and have an important instructive significance for establishing a uniform framework of set-based granular computing.