Rough set theory is an important non-numeric method for dealing with uncertainty and data mining. In this paper, we study rough sets and rough fuzzy sets on two universes via covering models. We introduce a new definition for the lower and upper approximation by taking a covering of the second universe of discourse. Some properties of the new model are revealed. We believe that this model will be more realistic in the sense that rough sets (resp. rough fuzzy sets) are approximated by sets (resp. fuzzy sets) on the same universe. Moreover, some results, examples and counter examples are provided.
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