Matrix theory for Binary Granular Computing

Matrix Theory-based Binary Neighborhood System is studied from view of Granular Computing (GrC). Granular Structure Matrix, Quotient Set Matrix, Quotient Structure Matrix, Granular Relation Matrix are defined to express basic definitions in Binary Granular Computing. Center knowledge based Topological definition for upper and lower approximation of binary relation is also defined and computed by matrix, it brings different explanation for knowledge approximation from that of Rough Set Theory. Binary Knowledge Representation System (B-KRS) is also built by matrices, this is the foundation for further knowledge discovery. Examples are given to illustrate the definitions.