基于模糊不变子群的上、下近似

The Upper and Lower Approximations Based on a Fuzzy Normal Subgroup

研究群中集合的粗糙近似问题。利用分解定理和表现定理,定义了群中集合关于模糊不变子群的上、下近似,并给出了近似算子的性质。证明了子群的上、下近似在同态映射下的不变性质。

This paper studies the approximations of sets in a group. By using the representation theorem and decomposition theorem in the theory of fuzzy set, we introduce the notions of upper and lower approximations of a set with respect to a fuzzy normal subgroup. Some basic properties of the approximation operators are examined. We also prove the invariant properties of the approximations of a subgroup under some homomorphisms.