The Research On The Theory And Application Of Grey Multi-granulation Rough Sets

With the development of science and technology,especially the rapid development of computer,industry and network prompt the exponential growth of data and information from various global fields,such as business,medical,industrial,financial and entertainment life.So,summarizing these huge amounts of data with uncertainty and finding the underlying valuable knowledge by scientific and effective methods have become a very important topic in intelligent information processing research.Multi-granulation rough set theory,as a kind of extended rough set theory can effectively deal with uncertainty problems,which uses granular computing and rough set theory to approximate the target decision and deal with uncertainty problems from a finer granularity space.The multi-granulation rough set theory has been widely used in feature selection,decision analysis and medical diagnosis.To explore multi-granulation rough set theory in the application of knowledge acquisition from uncertainty problems with grey information,and expand the application range of multi-granulation rough set theory,this paper focuses on uncertainty information systems with grey information,carries on some related researches by combining with grey system theory and multi-granulation rough set theory,the main work and innovations are as follows:1.The research background,significance and the research status of rough set theory and the research objectives of this paper are expounded.Then we illustrate the bottlenecks of rough set theory's application and the limitations of multi-granulation rough set theory,which motive us to do this research.After that,we sketch the arrangement of this thesis and provide a brief description of some important basic knowledge about dealing with uncertainty information.2.In order to deal with uncertainty problems with grey information,we combine with grey system theory to define grey granular structure,and then optimistic grey multi-granulation rough set(OGMGRS)and pessimistic grey multi-granulation rough set(PGMGRS)models are devised.Then we discuss several important properties of OGMGRS and PGMGRS.Meanwhile,we construct new attribute reduction algorithm based on the PGMGRS.Theoretical studies and practical examples demonstrate that the proposed GMGRS models largely enrich the MGRS theory and extend the study range of MGRS.3.To effectively handle uncertainty problems with grey information,we devise a variable precision grey multi-granulation rough set(VPG-MGRS)with a threshold to control the number of grey granular structures under the framework of MGRS.Then,we discuss several important properties of VPG-MGRS and the relationships of OGMGRS and PGMGRS models.After that,we propose a new attribute reduction algorithm with redefining the significance measures of attribute based on the VPG-MGRS.Theoretical studies and numerical experiments have demonstrated that our proposed VPG-MGRS model has more wide applicability for dealing with grey information system,and further extend the study range of MGRS.4.A discernibility matrix attribute reduction method based on VPG-MGRS for inconsistent grey decision system is put forward.First,a definition for transforming inconsistent grey decision system into consistent grey decision system is proposed based on VPG-MGRS.To simplify the complex grey decision system,we propose a decision confidence conversion model.Based on that,we redefine the discernibility function to enumerate all reducts of the inconsistent grey decision system.Theoretical studies and numerical experiments have demonstrated that the proposed attribute reduction method can effectively reduce the computational complexity,and further extend the study range of GMGRS.