Best fuzzy partitions to build interpretable DSSs for classification in medicine

Decision Support Systems (DSSs) based on fuzzy logic have gained increasing importance to help clinical decisions, since they rely on a transparent and interpretable rule base. On the other hand, probabilistic models are undoubtedly the most effective way to reach high performances. In order to join positive features of both these two approaches, this work proposes a hybrid approach, consisting in transforming the functions describing posterior probabilities, into a combination of orthogonal fuzzy sets approximating them. The resulting fuzzy partition has double hopefulness: since it approximates posterior probabilities, it is able to model information extracted from a dataset in such a form that they can be used to run predictions, and since it is a set of normal, orthogonal and convex fuzzy sets, it can be interpreted as the set of terms of a linguistic variable. As a proof of concept, the method has been applied to a real-life application pertaining the classification of Multiple Sclerosis Lesions. The results show that this method is able to construct, for each one of the variables influencing the classification, interpretable if-then rules, with classification power comparable to that of a classical Bayesian model. © 2013 Springer-Verlag.