The Optimal Scale Selection For Generalized Multi-granular Labeled Decision Systems

Granular computing,proposed in the end of last century,is a new 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 optimal selection of granularities and relations among granules which are represented by granular IF-THEN rules with granular variables and their relevant granular values.This dissertation deals with the related problems of representation of information granules in generalized multi-granular labeled information systems,optimal granular labeled selections and acquisition of decision rules in complete and incomplete generalized multi-granular labeled decision systems.Definition of generalized multi-granular labeled information systems,in which attributes may have different numbers of levels of granulations,is first introduced.Concepts of granular labeled selections in generalized complete multi-granular labeled information systems are then explored.Representations of information granules with their relationships under different granular labels are examined.Lower and upper approximations of sets determined by equivalence relations are further defined,and their properties are studied.Optimal granular labeled selections in generalized complete multi-granular labeled decision systems are also defined.Belief and plausibility functions in the Dempster-Shafer theory of evidence are employed to characterize optimal granular label selections in consistent generalized complete multi-granular labeled decision systems.Knowledge acquisitions in the sense of certain rule induction in consistent generalized complete multi-scale decision systems are explored.Finally,representations of information granules under different granular labeled selections in generalized incomplete information systems and approach to optimal granular labeled selections are also developed to knowledge acquisition in the sense of certain decision rules in consistent generalized incomplete multi-granular labeled decision systems.