Research on the model of rough set over dual-universes

To tackle the problem of rough set on single-universe, we discuss the rough set model over dual-universes in aspect of building connection between single-universe model and dual-universes model. The rough set model over dual-universes denoted as RSMDU in this paper is built through inspecting the relation between the two universes. Firstly, we propose the RSMDU and study its property using character function and relation matrix. The algorithm for obtaining the lower and upper approximations is then presented. Secondly, we show that Pawlak rough set model can be induced using RSMDU. The theorem inferring the connection between Pawlak model induced by RSMDU and RSMDU is presented. Finally, the applications of RSMDU are studied. According to proposed model, we demonstrate that the existing models of rough set are special cases of RSMDU and that the set of conditional attribute and the set of decision attribute can be regarded as dual-universes in decision-making system, where the model can be utilized to handle decision processing.