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Ontologies play an indispensable role in the Semantic Web by specifying the definitions of concepts and individual objects. However, most of the existing methods for constructing ontologies can only specify concepts as crisp sets. However, we cannot avoid encountering concepts that are without clear boundaries, or even vague in meanings. Therefore, existing ontology models are unable to cope with many real cases effectively. With respect to a certain category, certain objects are considered as more representative or typical. Cognitive psychologists explain this by the prototype theory of concepts. This notion should also be taken into account to improve conceptual modeling. While there has been different research attempting to handle vague concepts with fuzzy set theory, formal methods for measuring typicality of objects are still insufficient. We propose a cognitive model of concepts for ontologies, which handles both likeliness (fuzzy membership grade) and typicality of individuals. We also discuss the nature and differences between likeliness and typicality. This model not only enhances the effectiveness of conceptual modeling, but also brings the results of reasoning closer to human thinking. We believe that this research is beneficial to future research on ontological engineering in the Semantic Web.