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This paper deals with how people combine simple, prototype concepts into complex ones; e.g., how people combine the prototypes for brown and apple so they can determine the typicality of objects in the conjunction brown apple. We first consider a proposal from fuzzy-set theory (Zadeh, 1965), namely, that the typicality of an object in a conjunction is equal to the minimum of that object's typicality in the constituents (e.g., an object's typicality as a brown apple cannot exceed its typicality as a brown or as an apple). We evaluated this “min rule” against the typicality ratings of naive subjects in two experiments. For each of numerous pictured objects, one group of subjects rated its typicality with respect to an adjective concept, a second group rated its typicality vis-à-vis a noun concept, and a third group rated its typicality with respect to the adjective-noun conjunction. In both studies, most objects were rated as more typical of the conjunction than of the noun. These findings violate not only the min rule but also other simple rules for relating typicality in a conjunction to typicalities in the constituents. As an alternative to seeking such rules, we argue for an approach to conceptual combination that starts with the prototype representations themselves. We illustrate one version of this approach in some detail, and show how it accounts for the major findings of the present experiments.