Neighborhood Complementary Information Measures And Their Attribute Reductions Based On Three-layer Granular Structure

The information entropy system is an important theory for uncertainty characterization and approximate reasoning,and it has been introduced into rough sets for data analysis and intelligent processing.Classical complementary entropy,complementary conditional entropy,and complementary mu-tual information can effectively characterize the roughness and fuzziness of information.But at present,the neighborhood rough set has not involved the research of complementary entropy system.In addition,the classical complementary entropy system lacks hierarchy and smoothness,so its attribute reduction has application limitations.Therefore,the construction of neighborhood complementary entropy system and its attribute reduction has academic innovation and application value.In this regard,based on the three-layer granularity structure in the neighborhood system,this thesis extends the complementary entropy system to the neighborhood rough set,and hierarchically constructs the neighborhood complementary entropy system.Finally,the related attribute reduction is studied.Based on neighborhood expansion,the related informa-tion measures system and attribute reduction have uncertainty application prospects.The main research contents involve the following three aspects.(1)Based on the three-layer granularity structure of neighborhood system,and by using the granula-tion computing technology,the strategy of analytic simulation and information granulation replacement is implemented to expand and construct neighborhood complementary entropy system.Firstly,the entropy of neighborhood complementary,the entropy of neighborhood complementary condition and the mutual infor-mation of neighborhood complementary are defined at the Macro-Top level.Through the "decomposition extraction" of neighborhood complementary information measures of Macro-Top level,the Meso-Middle level information measures are obtained.By mathematic mathematical studies,the properties of system equation,double-bounds characterization,granulation non-monotonicity,and system expansibility are obtained at two levels.(2)Based on neighborhood complementary entropy,neighborhood complementary conditional entropy,and neighborhood complementary mutual information,the non-monotonic attribute reduction is proposed.Furthermore,the heuristic classification attribute reduction algorithm is designed at the Macro-Top level;the heuristic class attribute reduction algorithm is designed at the Meso-Middle level;the examples of decision tables are used to verify the correctness of the measures properties and the effectiveness of the algorithm calculations.(3)The implementation of UCI data experiments at the Macro-Top level and the Meso-Miiddle level specifically verify the granulation non-monotonicity of the neighborhood complementary information mea-sures.Furthermore,the effectiveness of the classification attribute reduction heuristic algorithm and the class attribute reduction heuristic algorithm is verified.