Learning Concurrently Granularity, Membership Function Parameters and Rules of Mamdani Fuzzy Rule-based Systems

In this paper we tackle the issue of generating Mamdani fuzzy rule-based systems with optimal trade-offs between complexity and accuracy by using a multi-objective genetic algorithm, which concurrently learns rule base, granularity of the input and output partitions and membership function parameters. To this aim, we exploit a chromosome composed of three parts, which codify, respectively, the rule base, and, for each variable, the number of fuzzy sets and the parameters of a piecewise linear transformation of the membership functions. We show the encouraging results obtained on a real world regression problem. Keywords— Accuracy-Interpretability Trade-off, Granularity Learning, Mamdani Fuzzy-Rule-Based Systems, Multi-objective Evolutionary Algorithms, Piecewise Linear Transformation.