Summary: We use neighbourhood spaces as the ranges of arbitrary hazy structures imposed on the set of truth values in a multiple-valued logic instead of pointwise truth values. In light of this consideration, we can characterize and modify the indistinguishable formulas of the propositional or first-order multiple-valued logics. Thus, any problem in any ordinary \(m\)-valued logic, for instance the problem of realizability of a formula \(\varphi\), can be reduced to that of a corresponding problem in \(n\)-valued logic where \(m\) might be a finite or transfinite ordinal number and \(n\leq m\), that is to say that we can reduce the denumerable or even continuum-valued logics to a finite \(n\)-valued logic such as Łukasiewicz 3-valued logic. In the final part of the paper we use neighbourhood systems or hazy structures for necessities and possibilities as relevant examples.