Interpretability Constraints for Fuzzy Modeling Implemented by Constrained Particle Swarm Optimization
George E. Tsekouras, John Tsimikas, Christos Kalloniatis, Stefanos Gritzalis · IEEE Transactions on Fuzzy Systems · 2017
In this paper certain interpretability criteria are taken into account in order to extract a set of linear inequality constraints for enhancing the fuzzy model interpretability. Among others, the criteria of model distinguishability, completeness, compactness, and fuzzy set sharing between rules are considered. To support distinguishability, the distances between fuzzy set centers are lower bounded and the widths are manipulated as to control the overlap between fuzzy sets. Sufficient conditions are given to satisfy the completeness criterion, whereas the compactness requirement is addressed by comparing models with different number of rules. Finally, fuzzy set sharing between rules is achieved through a model optimization procedure that involves fuzzy set merging. It turns out that the feasible region is a compact and convex set. The tradeoff between interpretability and accuracy is established by minimizing the model's square error over the feasible region through constrained particle swarm optimization. The method is tested using a number of high-dimensional datasets and conducting two kinds of experiments. The first focuses on interpretability. The second studies the accuracy by comparing the method to other algorithms that perform unconstrained optimization, using nonparametric statistics.