Modeling the real world for data mining: granular computing approach

In logic, a "real world" is modeled by a Cantor set with relational structure. In this paper, the relational structure is confined to the simplest kind, namely, binary relations. From different consideration, in granular computing, such a binary relational structure has been called a crisp/fuzzy binary granulation, or binary neighborhood system (FBNS). Intuitively, the set has been granulated into binary neighborhoods (generalized equivalence classes). Combining the two views, the simplest kind of "real world" model is BNS-space. From this view, the classical relational theory is the knowledge representation of the universe whose structure is a finite set of equivalence relations; in a "real world" relational theory, a finite set of crisp/fuzzy binary relations. Here knowledge representation is assigning meaningful names to binary neighborhoods (or equivalence classes in relational theory). Depending on the structures, the model can be useful in fuzzy logic or data mining. The focus of this paper is on data mining using granular computing. Experiments show that the computing is extremely fast and the cost of computing extra semantics is very small.