Application Of Matrix In Granular Computing And Three-way Concepts Research

In the research of granular computing,there is less research on granular structure of incidence relations;in addition,there are fewer methods in the construction of three-way concepts in the research of three-way concept lattice.Therefore,this paper will use matrix to discuss granulation computing and the construction of three-way concepts for the above two problems.Firstly,application of matrix in granulation of incidence relations:The problem of incidence relation merging can be regarded as a merging problem of incidence relations in undirected graphs with data points as vertices and relation among data points as edges.Since there is a one-to-one correspondence between graph and matrix under the sense of isomorphism,the problem of incidence merging in an undirected graph can be considered by a matrix way.This paper defines the correlative definitions of associated-combinatorial structure and granular structure and the corresponding matrix under the combination problem of incidence relations.According to the correlation between associated-combinatorial structure and granulation structure,a method of obtaining the correlation matrix of granulation structure from the correlation matrix of associated-combinatorial structure is given.Simultaneously,the above method is applied to the problem of how to adjust the dispatching station after the combination of highway routes.Secondly,two applications of matrix in the construction of three-way concepts:First,a formal context can be regarded as a matrix consisting of objects as rows and attributes as columns.By studying the relationship of intents(extents)between classical formal concepts,the principle of vertical(horizontal)merging between classical formal concepts is defined.And it gives algorithm to obtain attribute-induced(object-induced)three-way concepts according to the principle of vertical(horizontal)merging.Examples are given to illustrate the algorithms,and the feasibility of algorithms are verified,respectively.Second,based on formal context,positive and negative operator operations are performed on each attribute.According to the operation results,attribute matrix is defined,and attribute-induced three-way concepts are constructed according to the matrix.Correspondingly,positive and negative operator operations are performed on each object to define the object matrix,and according to the matrix structure,object-induced three-way concepts are obtained.Algorithms are given to obtain attribute-induced three-way concepts and,respectively.The feasibility and validity of the two algorithms are verified by examples.