Fuzzy probabilistic rough set model on two universes and its applications

The classical probabilistic rough set model is established based on a crisp binary relation. As a generalization of crisp binary relation, fuzzy relation makes descriptions of the objective world more realistic, practical, and accurate in some cases. Thus probabilistic rough set model based on a crisp binary relation limits its application domain. In this paper, based on a fuzzy relation, we propose a fuzzy probabilistic rough set model on two universes. Meanwhile, the concepts of the inverse lower and upper approximation operators are presented. We also study some properties of these approximation operators. Finally, a numerical example of the clinical diagnosis systems is applied to illustrate the validity of the proposed model. And we compare the proposed model with other models to show the superiority of the proposed model.