Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions

Rough set models on two universes are valuable generalizations of classic rough set model. These models can be applied into formal concept analysis and decision-making system. This paper focuses on catoptrical approach for rough set models over two universes using granule-based definition. In this paper, we propose a new catoptrical rough set model over dual universes. The properties of the proposed model are discussed. Consequently, a variable precision extension of the model is presented. Some properties of the extended model are obtained. Finally, we investigate a further extension of the proposed model, i.e. variable precision catoptrical rough set model with two parameters.