Fuzzy covering-based rough set on two different universes and its application

In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in paper. First, present definition $$\beta$$ -neighborhood, which can be seen as mapping from universe to sets on another and study its properties. Then define investigate properties model. Meanwhile, give necessary sufficient condition under -coverings generate same covering lower approximation or upper approximation. Moreover, matrix representations operators are investigated. Finally, approach kind multiple criteria decision making problem based universes. The proposed models not only enrich theory but also provide perspective for with uncertainty.