Evolutionary multi-objective optimization of fuzzy rule-based classifiers in the ROC space

An approach to select the most suitable fuzzy rule-based binary classifier to a specific application is proposed. First, an evolutionary three-objective optimization algorithm is applied to generate an approximation of a Pareto front composed of fuzzy rule-based binary classifiers with different trade-offs between accuracy and complexity. Accuracy is measured in terms of sensitivity and specificity, whereas complexity is computed as sum of the conditions which compose the antecedents of the rules included in the classifiers. Thus, low values of complexity correspond to fuzzy systems characterized by a low number of rules and a low number of input variables actually used in each rule. This ensures a high comprehensibility of the classifiers. Then, the most suitable classifier is selected by using the ROC convex hull method. We discuss the application of the proposed approach to generate a classifier for discriminating lung nodules from non-nodules in a computer aided diagnosis (CAD) system. Results obtained on a real data set extracted from lung CT images are also discussed