Combination of Interpretable Fuzzy Models and Probabilistic Inference in Medical DSSs

Fuzzy logic have gained increasing importance in Decision Support Systems (DSSs), in particular in medical field, since it allows to build a transparent and interpretable knowledge base. However, in order to obtain a general description of a system, probabilistic approaches undoubtedly offer the most significant information. Moreover, a good system should be useful also to classify data items which are lacking of some input features. In this work, an approach is proposed to construct an interpretable fuzzy system, which furnishes probabilistic information as a result. The resulting fuzzy sets can be interpreted as the terms of the involved linguistic variables, while the resulting weighted rules model probabilistic information. Rules are presented in two forms: the first is a set of one-dimensional models, which can be used if only one input feature is known; the second is a multi-dimensional combination of them, which can be used if more input features are known. As a proof of concept, the method has been applied for the detection of Multiple Sclerosis Lesions from brain images. The results show that this method is able to construct, for each one of the variables influencing the classification, an interpretable fuzzy partition, and very simple if-then rules. Moreover, a multi-dimensional rule base is presented, by means of which improved results are obtained, also with respect to naive Bayes classifier.