  We examine double successive approximations on a set, which we denote by
$L_2L_1, \ U_2U_1, U_2L_1,$ $L_2U_1$ where $L_1, U_1$ and $L_2, U_2$ are based
on generally non-equivalent equivalence relations $E_1$ and $E_2$ respectively,
on a finite non-empty set $V.$ We consider the case of these operators being
given fully defined on its powerset $\mathscr{P}(V).$ Then, we investigate if
we can reconstruct the equivalence relations which they may be based on.
Directly related to this, is the question of whether there are unique solutions
for a given defined operator and the existence of conditions which may
characterise this. We find and prove these characterising conditions that
equivalence relation pairs should satisfy in order to generate unique such
operators.
