Roughness bounds in rough set operations

The propagation and combination of uncertainties can significantly influence the performance of an information system. Although there have been great efforts in the propagation of randomness, fuzziness and other uncertainties, there is not yet a thorough study for the propagation of roughness in rough set operations. The derivation of a roughness bound for various rough set operations is given. We proved that there is no defined bound for the intersection operation of any two rough sets but there are bounds for union, complement and most difference operations. This is beneficial for decision making involving large volumes of rough set operations