Research On Methods Of Updating Formal Concept And Selecting Granularity Under Covering Multi-granularity

Formal concept analysis is a method of data analysis and knowledge discovery in formal context,this theory is supported by the solid mathematical foundation,and its core tool is formal concept generated according to the binary relationship between objects and attributes in formal context.Multi-granularity formal concept analysis is a method of data analysis and knowledge discovery that combines multi-granularity thought with formal concept analysis to analyze data from multiple perspectives and levels to solve specific complex data in reality.According to the method of attribute granulation,multi-granularity formal concept analysis is divided into formal concept analysis under partition multi-granularity and covering multi-granularity.Formal concept analysis under covering multi-granularity is more suitable for dealing with the complex granulation relationship in real life.In this paper,we study methods of updating formal concept and selecting optimal granularity under covering multi-granularity.Under covering muti-granulation,attributes in formal context have different levels of granularity,and accordingly,the derived concept lattice may reveal information and patterns at different granularities.Therefore,the ability to change the granularity level of attributes in formal concept analysis to capture relevant patterns in data and the ability to select the optimal granularity level of attributes are two natural requirements.The realization of the method of updating formal concept under covering multi-granularity can avoid the huge computational time cost of constructing the large-scale concept structure of formal context through complete reconstruction.At the same time,in multi-granularity formal context,selecting the appropriate attribute granularity to generate accurate,interesting,and redundant concept knowledge and information can also avoid the huge computational cost of changing the granularity level of attributes many times to capture the relevant patterns in the data.In a word,the research in this paper provides a solid foundation for the theoretical research of multi-granularity formal concept analysis.The main achievements of this paper are as follows:(1)The method of updating formal concept under covering multi-granularity is realized.Firstly,it is proved that the existing concept coarsening and updating algorithm will lead to concept deletion,and the concept coarsening algorithm is supplemented and improved by analyzing the characteristics of missing concepts.Secondly,it is proved that the existing concept refinement and updating algorithms will generate redundant concepts,the time complexity is high,so the existing concept refinement updating algorithm is optimized,and the performance advantages of the concept refinement algorithm proposed in this paper are verified by time complexity analysis and comparative experiments.(2)The method of selecting the optimal granularity under covering multi-granularity is realized.Firstly,based on the covering granularity method of attributes,multi-granularity formal context and multi-granularity formal decision context are defined,and rough approximation and belief structure in multi-granularity formal context are also defined.Secondly,based on granule consistency,the selection method of optimal granularity combination of attributes in granule consistent multi-granularity formal decision context is studied,and it is proved that the optimal granularity combination of attributes can be characterized by the belief function in evidence theory.Finally,based on rough set theory and evidence theory,this paper gives six methods of selecting the optimal granularity combination of attributes in granule inconsistent multi-granularity decision formal context,and analyzes the relationship between the six optimal granularity combinations of attributes.