Abstract: Rough set theory, proposed by Z. Pawlak, has evoked a lot of researches. Theoretic study has included algebra aspect of rough sets. The concept of rough group is introduced firstly by R. Biswas and S. Nanda, but with some deficiencies remaining. The concept of rough group is improved by other researchers. Based on a new revision of rough group, this paper presents three concepts, namely, order of rough group, order of element in rough group, and rough cyclic group. Synchronously it provides some properties of theirs. Besides, it is explained that some conclusions, which are correct in cyclic group, are not correct in rough cyclic group by means of some examples.

Key words: rough set, group, rough group, rough cyclic group

摘要： 自Z.Pawlak提出粗糙集理论以来，众多学者进行了广泛深入的研究，将其拓展至粗糙代数领域。R.Biswas和S.Nanda首次提出了粗糙群（B-N粗糙群）的概念并给出了若干性质，但这一概念本身存在一定缺陷。已有一些研究者指出了B-N粗糙群的定义和结论存在的一些问题，给出了B-N粗糙群的修正定义。以粗糙群的修正定义为基础，提出了粗糙群的阶、粗糙群元素的阶以及粗糙循环群等概念，给出了与之相关的一些性质，通过实例说明了普通循环群的某些性质对粗糙循环群并不成立。

关键词: 粗糙集, 群, 粗糙群, 粗糙循环群