Roughness Bounds in Set-oriented Rough Set Operations

Roughness is an important indicator for the uncertainty of a rough set. This paper analyses the roughness bounds for set-oriented rough set operations. A bound of the roughness of the union between two set-oriented rough sets could be determined by the roughness of the two operand set-oriented sets. In most cases, a bound could also be found for a difference set between two set-oriented rough sets. However, the roughness of the operand sets can not uniquely bound the roughness of their intersection set. The results presented here show that a bound of the set operation can be determined from their operand´s roughnesses under some operations. We provide an example to show the derived bounds from operand´s roughness.