We consider comparative dissimilarity relations on pairs on fuzzy description profiles, the latter providing a fuzzy set-based representation of pairs of objects. Such a relation expresses the idea of “no more dissimilar than” and is used by a decision maker when performing a case-based decision task under vague information. We first limit ourselves to those relations admitting a weighted Lp distance representation, for which we provide an axiomatic characterization in case the relation is complete, transitive and defined on the entire space of pairs of fuzzy description profiles. Next, we switch to the more general class of comparative dissimilarity relations representable by a Choquet Lp distance, parameterized by a completely alternating normalized capacity.