Exploiting Particle Swarm Optimization to Attune Strong Fuzzy Partitions Based on Cuts

Cut-based strong fuzzy partitions (SFP) are characterized by cuts, i.e. points in the universe of discourse where the non-zero membership degrees of the fuzzy sets in the partition is 0.5. Cuts are useful to identify the most representative regions for the fuzzy sets involved in a SFP but pose loose constraints on the slopes of trapezoidal fuzzy sets. We address the problem of optimizing such slopes in order to maximize the performance of fuzzy rule-based systems while keeping cuts constant. This way, model performance is improved and interpretability is preserved. We use Particle Swarm Optimization to perform optimization and we analyze two different approaches for generating solution spaces. We tested the proposed approach on a number of fuzzy rule-based classifiers designed by DC* on synthetic data. For all the considered models, performance is never degraded but improved in many cases, without violating any interpretability constraint.