Three-way reduction for formal decision contexts

Attribute reduction is an important component in rough set theory and formal concept analysis. The three-way concept lattice is a combination of concept lattices and threeway decision theory. We investigate granular reduction, three-way granular reduction, and three-way distribution reduction for general formal decision contexts. We furthermore obtain discernibility matrix-based reduction algorithms for each type of reduction. In particular, we demonstrate that in decision contexts, three-way granular reduction coincides with positive region reduction for decision tables. Furthermore, we evaluate the effectiveness of the three-way granular reduction algorithm using 17 UCI datasets.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

Attribute reduction is an important component in rough set theory and formal concept analysis, and the three-way concept lattice is a combination of concept lattices and three-way decision theory. This paper investigates granular reduction and distribution reduction in general formal decision contexts, and proposes reduction algorithms based on discernibility matrix for each type of reduction. The effectiveness of the three-way granular reduction algorithm is evaluated using 17 UCI datasets.