Approximation of statistical information with fuzzy models for classification in medicine

Fuzzy logic have gained increasing importance in Decision Support Systems (DSSs), in particular in medical field, since it allows to build a transparent and in-terpretable knowledge base. However, in order to obtain a general description of a system, probabilistic approaches undoubtedly offer the most significant infor-mation. Moreover, a good classifier to be used for medical scopes should be able to: i) classify data items which are lacking of some input features; ii) extract knowledge from incomplete datasets; iii) consider categorical features; iv) give re-sponses in terms of a set of possible classes with respective degrees of plausibil-ity. The approach here proposed pursues and achieve these objectives by approx-imating probabilistic information from incomplete datasets with an interpretable fuzzy system for classifying medical data. Resulting fuzzy sets can be interpreted as the terms of the involved linguistic variables, corresponding to numerical and/or categorical features, while 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. 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, multi-dimensional rule bases can be constructed, by means of which improved results are obtained, also with respect to naive Bayes classifier.