A Partition Model of Granular Computing

There are two objectives of this chapter. One objective is to examine the basic principles and issues of granular computing. We focus on the tasks of granulation and computing with granules. From semantic and algorithmic perspectives, we study the construction, interpretation, and representation of granules, as well as principles and operations of computing and reasoning with granules. The other objective is to study a partition model of granular computing in a set-theoretic setting. The model is based on the assumption that a finite set of universe is granulated through a family of pairwise disjoint subsets. A hierarchy of granulations is modeled by the notion of the partition lattice. The model is developed by combining, reformulating, and reinterpreting notions and results from several related fields, including theories of granularity, abstraction and generalization (artificial intelligence), partition models of databases, coarsening and refining operations (evidential theory), set approximations (rough set theory), and the quotient space theory for problem solving.