A short note on rough set over dual-universes

Abstract

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.

Keywords::

• rough set
• rough set extension on universes
• compatibility relation
• rough set over dual-universes

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 71301100], [grant number 11226240], the National Society Science Foundation of China [grant number 12BGLo88], Innovation Program of Shanghai Municipal Education Commission [grant number 14YZ140], [grant number 14YS119], the Natural Science Foundation of Jiangsu Province of China [grant number BK2012469] and the Doctorate Foundation of Shanghai [grant number 11692191400].