Three-way decision on two universes

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 alpha and beta. Our approach is based on the maximum value of the accuracy measure with respect to tri-partitions of a universe induced by all thresholds. (C) 2019 Elsevier Inc. All rights reserved.