Abstract
Rough set models on two universes are important generalizations of Pawlak’s classical model. In most of the two-universe models, the upper and lower approximations are constructed based on inclusion relation. We generalize inclusion relation to the general evaluation function and define the models of three-way decision on two universes. As an important class of evaluation functions, subsethood measures are considered. We compare our models with other five existing two-universe models in rough set theory and point out that the model of three-way decision on two-universe unifies the five two-universe models. Besides, properties of the two-universe model of three-way decision are also given. More importantly, we propose an approach to computing the pair of thresholds α and β. Our approach is based on the maximum value of the accuracy measure with respect to tri-partitions of a universe induced by all thresholds.
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