关键词: 粗糙集, 群, 粗糙群, 粗糙循环群

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