In this paper,we first introduce the concept of rough set in Q-algebra,discuss a series of important proper-ties of rough set in Q-algebra,and introduce rough set theory into Q-algebra.Secondly,the definition of rough ideal in Q-algebra is proposed,and the relationship between ideal and rough ideal in Q-algebra is discussed.Finally,the concept of weak congruence in Q-algebras is introduced,and some characterizations of weak congruence are obtained.It is proved that the set of all upper rough ideals in Q-algebras is dcpo,and the set of all lower rough ideals in Q-alge-bras is algebraic lattice.
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