An Attribute Reduction Algorithm for Concept Lattice Based on Discernible Boolean Matrix

Attributes of Concept Lattice are divided into absolutely necessary, relatively necessary and absolutely superfluous attributes. The discernible Boolean matrix of Concept Lattice and the elementary row transformation of Boolean matrix are defined. The model of attribute reduction in the form of linear logical equations is established. The method of transforming discernible Boolean matrix into simplest matrix by the elementary row transformation of Boolean matrix is proposed. And the necessary and sufficient condition for determining whether the attribute is absolutely necessary, relatively necessary and absolutely superfluous is given. Finally, an elementary intuitionistic attribute reduction algorithm is proposed by these necessary and sufficient conditions.