In many applications, such as case based reasoning, data mining or analogical reasoning, the choice of a particular measure of similarity is crucial. In this paper, we propose to study similarity measures from the point of view of the ordering relation they induce on object pairs. Using a classic method in measurement theory, introduced by Tversky, we establish necessary and sufficient conditions for the existence of a specific numerical measure, or a class of measures, to represent a given ordering relation, depending on the axioms this relation satisfies. The interest is particularly focused on different conditions of independence.