The dual block relation matrix of Boolean matrix and tolerance relation of row and column space lattice

Block relation and tolerance relation are important contents in formal concept analysis, which are widely used in knowledge discovery and data analysis. The definition of dual block relation matrix of Boolean matrix is given from the perspective of relation matrix. It is proved that the lattice formed by the dual block relation matrix of Boolean matrix is isomorphic to the lattice formed by all tolerance relations on the row and column space lattice of the Boolean matrix, and the quotient lattice induced by tolerance relation is isomorphic to the row and column space lattice of the dual block relation matrix of Boolean matrix.