Implementation of Rough Set on A Group Structure

Let  be a non-empty set and  an equivalence relation on . Then,  is called an approximation space. The equivalence relation on  forms disjoint equivalence classes. If , then we can form a lower approximation and an upper approximation of . If X⊆U, then we can form a lower approximation and an upper approximation of X. In this research, rough group and rough subgroups are constructed in the approximation space  for commutative and non-commutative binary operations.