Property of Rough Ideals in Semigroups

This article is based on the notions and the properties of a rough subsemigroup, rough left ideal,rough right ideal,rough two-sided ideal and rough bi-ideal in a semigroup.It combines the upper and lower approximations in a set satisfy the monotony, discussing some properties of the product of these two subsets in semigroups according to the properties of some especial single subsets such as subsemigroup and ideal, then the rigorous proof was given.Thus the rough theory in semigroups are completed and perfected.