A Three-Objective Evolutionary Approach to Generate Mamdani Fuzzy Rule-Based Systems

In the last years, several papers have proposed to adopt multi-objective evolutionary algorithms (MOEAs) to generate Mamdani fuzzy rule-based systems with different trade-offs between interpretability and accuracy. Since interpretability is difficult to quantify because of its qualitative nature, several measures have been introduced, but there is no general agreement on any of them. In this paper, we propose all MOEA to learn concurrently rule base and membership function parameters by optimizing accuracy and interpretability, which is measured in terms of number of conditions in the antecedents of rules and partition integrity. Partition integrity is evaluated by using a purposely-defined index based on the piecewise linear transformation exploited to learn membership function parameters. Results on a real-world regression problem are shown and discussed.