A simple discernibility matrix for attribute reduction in formal concept analysis based on granular concepts

Attribute reduction is one of the crucial issues in Formal Concept Analysis. Discernibility matrix plays an important role in attribute reduction, and has been achieved many successful applications in different concept lattice models. Nevertheless, it requires the construction of the concept lattice before the discernibility matrices are computed when applying traditional approaches, which is both time and space consuming. Furthermore, in some discernibility matrices, the comparisons between every two concepts result in a high computation complexity. To address these problems, granular concepts, i.e., the object concepts and the attribute concepts, are considered in this paper, and a simple discernibility matrix named Object-Attribute discernibility matrix is proposed. It averts the construction of the whole concept lattice and the comparisons between every two concepts. Consequently, the time complexity is greatly reduced, and a lot of storage space can also be saved. Theoretical analysis and experimental results show the efficiency of Object-Attribute discernibility matrix.