On the use of Measures of Separability of Classes to Characterise the Domains of Competence of a Fuzzy Rule Based Classification System

In this work we study the behaviour of a Fuzzy Rule Based Classification System, and its relationship to a certain data complexity measures family. As Fuzzy Rule Based Classification System we have selected a recent proposal called Positive Definite Fuzzy Classifier, which is a Fuzzy System that uses Support Vector Machines for its training, obtaining accurate results and a low number of rules. We have examined several data complexity metrics of separability of classes over a wide range of data sets built from real data, and try to extract behaviour patterns from the results for this learning method. Using these data complexity measures and the accuracy results of the Positive Definite Fuzzy Classifier, we have built a rule set which describes both good or bad behaviours of this Fuzzy Rule Based Classification System. These rules use different values of such data complexity measures as antecedents, so we aim to predict the behaviour of the method from the data set complexity metrics prior to its application. Therefore, the rule set could characterise the domains of competence of this particular Fuzzy Rule Based Classification System. Keywords— Classification, Data complexity, Fuzzy Rule Based Systems, Support Vector Machines