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The largest class of multivalued systems satisfying ring-like
axioms is the $H_v$-ring. Let $R$ be an $H_v$-ring and $\gamma^*$
be the smallest equivalence relation on $R$ such that the quotient
$R/\gamma^*$, the set of all equivalence classes, is a ring. In
this paper we consider the relation $\gamma^*$ defined on $R$ and
define the lower and upper approximations of a subset $A$ of $R$
with respect to $\gamma^*$. We interprete the lower and upper
approximations as subsets of the ring $R/\gamma^*$ and we prove
some results in this connection. In particular, we show that if
$A$ is an $H_v$-ideal of $R$ then upper approximation of $A$ is an
ideal of $R/\gamma^*$.
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