A short note on some properties of rough groups

  • Authors:

  • Changzhong Wang;Degang Chen

  • Affiliations:

  • Department of Mathematics, Bohai University, Jinzhou, Liaoning, 121000, PR China;Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

It is a useful method in research of group theory to construct a new group by using known groups. Lower and upper approximation operators of rough sets are applied into group theory and so the notion of a rough group has been introduced. In this paper, we first point out that there are still some incomplete propositions in [N. Kuroki, P.P. Wang, The lower and upper approximations in a fuzzy group, Inform. Sci. 90 (1996) 203-220] although some authors have showed several incorrect statements in the literature. We then present improved versions of the incomplete propositions and continue to study the image and inverse image of rough approximations of a subgroup with respect to a homomorphism between two groups.