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Medical decision making can be regarded as a process, combining both analytical cognition and intuition. It involves reasoning within complex causal models of multiple concepts, usually described by uncertain, imprecise, and/or incomplete information. Aiming to model medical decision making, we propose a novel approach based on cognitive maps and intuitionistic fuzzy logic. The new model, called intuitionistic fuzzy cognitive map (iFCM), extends the existing fuzzy cognitive map (FCM) by considering the expert's hesitancy in the determination of the causal relations between the concepts of a domain. Furthermore, a modification in the formulation of the new model makes it even less sensitive than the original model to missing input data. To validate its effectiveness, an iFCM with 34 concepts representing fuzzy, linguistically expressed patient-specific data, symptoms, and multimodal measurements was constructed for pneumonia severity assessment. The results obtained reveal its comparative advantage over the respective FCM model by providing decisions that match better with the ones made by the experts. The generality of the proposed approach suggests its suitability for a variety of medical decision-making tasks.