Complementary Information Measures Based on Three-layer Granular Structures

The measures with three-layer granular structure are the basis of three-layer attribute reduction and machine learning. In the rough set, starts from three-way probabilistic perspectives, the three-way weighted complement-entropies are established by combining different probability products and complementary information, which takes into account the decision table's three-layer granular structures and three-way probabilities. In the neighborhood rough set, this existed neighborhood complement-entropies adopt the complementary mechanism and relate to covering granulation, but don't involve three-way probabilities. In this paper, we mainly presented three-layer algorithms based on three-way neighborhood probabilistic complement-entropies from the Micro-Bottom and Macro-Top. And it also discussed the relationships of complement information measures, namely the three-way neighborhood probabilistic complement-entropies are equivalent to the existing neighborhood complement-entropies, and degenerate into three-way weighted complement-entropies.