Measurement and expert estimates are never absolutely accurate. Thus, when we know the result M(u) of measurement or expert estimate, the actual value A(u) of the corresponding quantity may be somewhat different from M(u). In practical applications, it is desirable to know how different it can be, i.e., what are the bounds f(M(u)) <= A(u) <= g(M(u)). Ideally, we would like to know the tightest bounds, i.e., the largest possible values f(x) and the smallest possible values g(x). In this paper, we analyze for which (partially ordered) sets of values such tightest bounds always exist: it turns out that they always exist only for complete lattices.