Granularity Selections in Generalized Incomplete Multi-Granular Labeled Decision Systems

Granular computing (GrC), which imitates human being’s thinking, is an approach for knowledge representation and data mining. Its basic computing unit is called granules, and its objective is to establish effective computation models for dealing with large scale complex data and information. The main directions in the study of granular computing are the construction, interpretation, representation of granules, the selection of granularities and relations among granules which are represented by granular IF-THEN rules with granular variables and their relevant granular values. In order to investigate knowledge acquisition in the sense of decision rules in incomplete information systems with multi-granular labels, the concept of generalized incomplete multi-granular labeled information systems is first introduced. Information granules with different labels of granulation as well as their relationships from generalized incomplete multi-granular labeled information systems are then represented. Lower and upper approximations of sets with different levels of granulation are further defined and their properties are presented. The concept of granularity label selections in generalized incomplete multi-granular labeled information systems is also proposed. It is shown that the collection of all granularity label selections forms a complete lattice. Finally, optimal granular label selections in incomplete multi-granular labeled decision tables are also discussed. Belief and plausibility functions in the Dempster-Shafer theory of evidence are employed to characterize optimal granular label selections in consistent incomplete multi-granular labeled decision systems.