Affiliations: Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2, Canada. [email protected] | Department of Computer Science and Technology, Tongji University, Shanghai, China 201804, China. [email protected] | Department of Computer Science and Technology, Tongji University, Shanghai, China 201804, China. [email protected] | Department of Computer Science and Technology, Tongji University, Shanghai, China 201804, China. [email protected]
Note: [] Address of corresponding author: Room 501, School of Electronics and Information Engineering, Tongji University, Shanghai, China 201804. Also works: Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2, Canada
Abstract: A framework is proposed for studying a particular class of set-theoretic approaches to granular computing. A granule is a subset of a universal set, a granular structure is a family of subsets of the universal set, and relationship between granules is given by the standard set-inclusion relation. By imposing different conditions on the family of subsets, we can define several types of granular structures. A number of studies, including rough set analysis, formal concept analysis and knowledge spaces, adopt specific models of granular structures. The proposed framework therefore provides a common ground for unifying these studies. The notion of approximations is examined based on granular structures.
