Ordered Granular Labeled Structures and Rough Approximations

Granular computing, which imitates human beings thinking, is an approach for knowledge representation and data mining. Its basic computing unit is called granule, and its objective is to establish effective computation models for dealing with large scale complex data and information. In order to study knowledge acquisition in ordered information systems with multi-granular labels, rough set approximations based on ordered granular labeled structures are explored. The concept of ordered labeled structures is first introduced. A dominance relation on the universe of discourse from an ordered labeled structure is also defined. Dominated labeled blocks determined by the dominance relation are constructed. Ordered lower approximations and ordered upper approximations, as well as ordered labeled lower approximations and ordered labeled upper approximations of sets based on dominance relations, are then proposed. Properties of approximation operators are examined. It is further proved that the qualities of lower and upper approximations of a set derived from an ordered labeled structure are a dual pair of necessity measure and possibility measure. Finally, multi-scale ordered granular labeled structures are defined and relationships among rough approximations with different scales induced from multi-scale ordered granular labeled structures are discussed.