Similarity functions between sets and in particular, between intervals, are traditionally assumed to verify a monotonicity condition. It requires that if three sets (intervals) are ordered by inclusion, the similarity between the greatest and the smallest must be smaller than the similarity between the middle one and any of the other two. We find this property coherent but too weak since it does not require anything from triplets of sets that are not perfectly ordered. A condition introduced in the last years that involves the concept of infimum and supremum applies to every triplet of intervals and generalizes the classical axiom of monotonicity for similarities. Despite it is a logical and intuitive condition, it is easy to check that it is not satisfied for every similarity. In this contribution we focus on similarities defined from embeddings and more particularly, from two families of embeddings and we study if the two families of similarity measures obtained comply with the general condition of monotonicity introduced two years ago. A positive answer is obtained in all the cases studied.