Multi-granularity Computing For Incomplete Multi-scale Data

Multi-granularity computing,which simulates human being’s thinking,has become hot study in the field of granular computing.The main objective of multi-granularity computing is to build models for dealing with large scale data from various visual angles and by multilevels methods.Multi-scale data analysis and multi-granulation rough set are two typical models of multi-granularity computing.Data sets in multi-scale data analysis are called(generalized)multi-scale information systems,in which each object under the same attribute can take on different values at different levels of scales.A key issue in multi-scale data analysis is to select appropriate subsystems from a given(generalized)multi-scale information system for the final classification or decision.The combinations of scale levels of all attributes corresponding to these subsystems are said to be optimal scale combinations of the system.In this dissertation,to investigate knowledge acquisition from incomplete multi-scale data,optimal scale combination selections for incomplete generalized multi-scale decision systems are studied by combining multi-granulation rough sets,evidence theory and information entropy.The main contents are as follows:Firstly,seven types of optimal scale combinations in generalized multi-scale covering decision systems are defined,and their relationships are clarified in consistent and inconsistent generalized multi-scale covering decision systems,respectively.It is proved that there are two different kinds of optimal scale combinations in consistent generalized multiscale covering decision systems and four different types of optimal scale combinations in inconsistent generalized multi-scale covering decision systems.These results are then applied to optimal scale combination selection for incomplete generalized multi-scale decision systems and generalized multi-scale set-valued decision systems,respectively.Secondly,multi-granulation structures are introduced in incomplete generalized multiscale decision systems.Incremental updating mechanisms of multi-granulation rough sets with the scale coarsening and refinement are first investigated.Concepts of pessimistic upper and lower approximation optimal scale combinations based on pessimistic multi-granulation rough sets are then defined,and their properties are examined.Evidence-theory-based numerical algorithms for finding optimal scale combinations are further designed.Notions of optimistic upper and lower approximation optimal scale combinations based on optimistic multi-granulation rough sets are also introduced,and it is exemplified that there is no static relationship between optimistic upper and lower approximation optimal scale combinations.Finally,for a partially incomplete generalized multi-scale decision system in which attribute values of some objects are unknown at finer scales of attribute and deterministic at coarser ones,a method is proposed to transform such a system into a generalized multi-scale set-valued decision system.Concept of local conditional entropy of a single decision class with respect to attributes is introduced to characterize uncertainty of information granules in incomplete generalized multi-scale decision systems.Definitions of lower approximation optimal scale combination and local conditional entropy optimal scale combination of a single decision class are defined,and their relationships are further clarified.