Attribute reduction in formal contexts based on a new discernibility matrix

Abstract

The theory of concept lattices is an efficient tool for knowledge discovery. One of the key problems of knowledge discovery is knowledge reduction. This paper proposes a method based on a new discernibility matrix for reduction of concept lattices in formal contexts. The judgment theorem of consistent sets is examined and the Boolean function to calculate reducts is given. All the reducts of a formal context can be calculated by this discernibility matrix and Boolean function. It is proved that the approach claimed in this paper is equivalent to the well-accepted one proposed in Zhang et al. (Attribute Reduction in Concept Lattice Based on Discernibility Matrix. Lecture Notes in Computer Science, vol. 3642, pp. 157–165, 2005), and the former’s calculation amount is less than the latter’s. In addition, it shows that the essentiality of reduction is to keep the difference between any concept and its child-concepts.