A short note on rough set over dual-universes

To extend the utilisation and flexibility of rough set extension on universes, we modify rough set over dual-universes model by comparing rough set extension on universes based on compatibility relation and rough set over dual-universes in the aspect of theories and applications. Instance in daily life is advanced to indicate shortcomings of rough set extension on universes based on compatibility relation and rough set over dual-universes. The similarities and differences between rough set over dual-universes and rough set extension models on universes based on compatibility relation are analysed from the view of approximation operators. New lower and upper approximations of rough set over dual-universes are designed by introducing set-valued map. An improved rough set model is constructed. The conclusion is that rough set over dual-universes in this article has a standard description and could solve practical problems well compared with rough set extension models on universes based on compatibility relation.

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