Generalisation of roughness bounds in rough set operations

This paper investigates the general roughness bounds for rough set operations. Compared with set-oriented rough sets, the results prove that the same upper bound of the roughness for the union, difference and complement operation could be determined by the roughness of the two operand sets. However, the lower roughness bounds of set-oriented rough sets operations do not hold for other rough sets. We provide an example to show the derived bounds from the operand’s roughness.