Multi-objective Fuzzy Pattern Trees

This paper describes a multi-objective system for induction of fuzzy classifiers based on Fuzzy Pattern Trees. Fuzzy Pattern Trees is a tree-based hierarchical model, having as internal nodes, fuzzy logical operators and their leaves are composed by the combination of fuzzy terms and input attributes. For each class present in the problem a tree is created. Each tree will be a "logical class description" allowing the interpretation of the result. The construction method of the original trees was replaced by the Cartesian Genetic Programming, to explore the search space better. Two objectives guide the search: the accuracy of the classification and the interpretability. Therefore the NSGA II multi-objective algorithm was used for search solutions that contemplate both. The proposed Classifier was compared with Random Forests, Support Vector Machines and K Nearest Neighbors in several databases of the UCI Machine Learning Repository presenting a competitive and interpretable result. Another comparison made was the proposed model, and the Fuzzy Pattern Trees initially proposed. The proposed model showed competitive results and smaller trees.