Rough Invariant Subgroup's Properties and Rough Quotient Group

Rough set theory is not only a new mathematical tool dealing with vagueness and uncertainty but also a new effective soft computing method. It was been widely used in the area of artificial intelligence, data mining, pattern recognition, decision analysis, fault diagnosis and so on. So according to the rough set theory and its extensive applications, the application of rough set theory to algebra system - group is discussed in this paper. Some properties of rough invariant subgroup and the concept of rough quotient group are introduced based on the basic concepts with respect to rough group, rough subgroup, rough invariant subgroup, some properties of rough subgroup, and some theorems of rough invariant group, meanwhile the rigorous proof is given.