Questions the metric and dimensional assumptions that underlie the geometric representation of similarity on both theoretical and empirical grounds. A new set-theoretical approach to similarity is developed in which objects are represented as collections of features and similarity is described as a feature-matching process. Specifically, a set of qualitative assumptions is shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features. Several predictions of the contrast model are tested in studies of similarity with both semantic and perceptual stimuli. The model is used to uncover, analyze, and explain a variety of empirical phenomena such as the role of common and distinctive features, the relations between judgments of similarity and difference, the presence of asymmetric similarities, and the effects of context on judgments of similarity. The contrast model generalizes standard representations of similarity data in terms of clusters and trees. It is also used to analyze the relations of prototypicality and family resemblance. (39 ref) (PsycINFO Database Record (c) 2016 APA, all rights reserved)