Abstract
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 three-way 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.
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