Rough set models in multigranulation spaces

There exist several approaches to rough set approximations in a multigranulation space, namely, a family of equivalence relations. In this paper, we propose a unified framework to classify and compare existing studies. An underlying principle is to explain rough sets in a multigranulation space through rough sets derived by using individual equivalence relations. Two basic models are suggested. One model is based on a combination of a family of equivalence relations into an equivalence relation and the construction of approximations with respect to the combined relation. By combining equivalence relations through set intersection and union, respectively, we construct two sub-models. The other model is based on the construction of a family of approximations from a set of equivalence relations and a combination of the family of approximations. By using set intersection and union to combine a family of approximations, respectively, we again build two sub-models. As a result, we have a total of four models. We examine these models and give conditions under which some of them become the same.