Matrix Entropy Reductions Of Decision Formal Context

Concept lattice is a structure for expressing hierarchical relationships among concepts.Attribute reduction is a method for knowledge representation and data processing in concept lattice,which has a wide range of applications in data mining,artificial intelligence,and information retrieval.For large-scale and mixed-type data,it is crucial to effectively perform attribute reduction on the dataset.Matrix is an efficient tool for data processing,which has been widely used in attribute reduction of various datasets.In this paper,the object particle,Boolean matrix and information entropy are connected,and matrix information entropy,matrix conditional entropy,matrix joint entropy and matrix mutual information entropy are constructed.This paper discusses matrix entropy reduction methods on formal contexts,matrix entropy consistent decision formal contexts(ME-consistent decision formal contexts)and matrix entropy inconsistent decision formal contexts(ME-inconsistent decision formal contexts).The specific research contents are as follows:(1)This paper introduces the concepts of matrix information entropy,matrix conditional entropy,matrix joint entropy,and matrix mutual information entropy by applying Boolean matrix,object granule,and information entropy,and discusses their properties and relationships.Based on the definition of matrix information entropy,this paper defines the importance of attributes in formal contexts and provides feature characterization and attribute reduction algorithms.The effectiveness of the proposed algorithms is verified by comparing them with UCI datasets.(2)This paper proposes the definitions of matrix information entropy,matrix conditional entropy,matrix joint entropy,and matrix mutual information entropy in the ME-coordinated decision formal context and studies their properties and relationships.In the ME-coordinated decision formal context,the concepts of coordinated set and reduction set based on matrix entropy are defined,and the concepts of internal and external importance of attributes are introduced,leading to feature characterization of attributes.A reduction method and algorithm based on matrix entropy are proposed.The proposed algorithm’s effectiveness is verified by comparing it with UCI datasets.(3)This paper defines the concepts of finite matrix information entropy,finite matrix conditional entropy,finite matrix joint entropy,and finite matrix mutual information entropy based on Boolean matrix,object granule,and information entropy,and analyzes their properties and relationships.Based on finite matrix entropy,the importance of attributes in the MEnon-coordinated decision formal context is characterized,and feature descriptions of various attributes are given,as well as finite matrix reduction methods and algorithms.The effectiveness of the proposed algorithms is verified by comparing them with UCI datasets.