Translates of Vague Groups

Abstract

As an abstraction of the geometric notation of translation, we introduce two operators T α+ and T α- called the vague translation operators. First we define the operators on vague sets and derive some of the properties .Then we investigate their action on vague groups, we prove that all translates of vague subgroups are vague normal sub groups [VNG], we observe that vague abelianness is not translation invariant. Subject classification:- 2000 AMS subject classification : 03G25 ,04A72 ,08A72 Keywords: α-increasing vague translation operator, α-decreasing vague translation operator ,vague translation groups ,translation of vague normal sub groups , vague conjugate property .