This paper introduces three classes of similarity measures for fuzzy description profiles, defined through the d-Choquet integral. Such classes of similarity measures are parameterized by the choice of a capacity and a restricted dissimilarity function, and generalize the classical Jaccard index for binary profiles. Semantics is added to such similarity measures on three different levels: (i) how common and different parts of profiles are aggregated (via the choice of the similarity functional form); (ii) how interactions among attributes are weighted (via the choice of the capacity); (iii) how pointwise dissimilarities are evaluated (via the choice of the restricted dissimilarity function).