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This chapter presents different notions used for fuzzy modelling that formalize fundamental concepts used in cognitive psychology. From a cognitive point of view, the tasks of categorization, pattern recognition or generalization lie in the notions of similarity, resemblance or prototypes. The same tasks are crucial in Artificial Intelligence to reproduce human behaviors. As most real world concepts are messy and open-textured, fuzzy logic and fuzzy set theory can be the relevant framework to model all these key notions. On the basis of the essential works of Rosch and Tversky, and on the critics formulated on the inadequacy of fuzzy logic to model cognitive concepts, we study a formal and computational approach of the notions of similarity, typicality and prototype, using fuzzy set theory. We propose a framework to understand the different properties and possible behaviors of various families of similarities. We highlight their semantic specifics and we propose numerical tools to quantify these differences, considering different views. We propose also an algorithm for the construction of fuzzy prototypes that can be extended to a classification method.