Design of interpretable fuzzy rule-based classifiers using spectral analysis with structure and parameters optimization

This paper presents a design method for fuzzy rule-based systems that performs data modeling consistently according to the symbolic relations expressed by the rules. The focus of the model is the interpretability of the rules and the model's accuracy, such that it can be used as tool for data understanding. The number of rules is defined by the eigenstructure analysis of the similarity matrix, which is computed from data. The rule induction algorithm runs a clustering algorithm on the dataset and associates one rule to each cluster. Each rule is selected among all possible combinations of one-dimensional fuzzy sets, as the one nearest to a cluster's center. The rules are weighted in order to improve the classifier performance and the weights are computed by a bounded quadratic optimization problem. The model complexity is minimized in a structure selection search, performed by a genetic algorithm that selects simultaneously the most representative subset of variables and also the number of fuzzy sets in the fuzzy partition of the selected variables. The resulting model is evaluated on a set of benchmark datasets for classification problems. The results show that the proposed approach produces accurate and yet compact fuzzy classifiers. The resulting model is also evaluated from an interpretability point of view, showing how the rule weights provide additional information to help data understanding and model exploitation.