A New view of the approximations in H _v -groups

Abstract

Let H is an H _v -group and $\mathcal{U}$ the set of all finite products of elements of H. The relation β^* is the smallest equivalence relation on H such that the quotient H/ β^* is a group. The relation β^* is transitive closure of the relation β, where β is defined as follows: x β y if and only if $\{ x,y \} \subseteq u$ for some $u \in \mathcal{U}$. Based on the relation β, we define a neighborhood system for each element of H, and we presents a general framework for the study of approximations in H _v -groups. In construction approach, a pair of lower and upper approximation operators is defined. The connections between H _v -groups and approximation operators are examined.