This paper proposes a set of minimal conditions which should be fulfilled by any multi-criteria additive procedure set out to work under imprecision. The proposed conditions are defined in terms of binary preference relations, which are inferred from interval-valued alternatives, and are shown to be useful for evaluating the interval-based reasoning procedures of imprecise multi-criteria methods. In particular, well-known distance-based methods like TOPSIS and VIKOR are examined in their interval
extensions, together with the interval-valued method of WOD, finding that only VIKOR fails to pass the complete test.