Multi-objective evolutionary generation of Mamdani fuzzy rule-based systems based on rule and condition selection

In the framework of multi-objective evolutionary fuzzy systems applied to regression problems, we propose to concurrently exploit a two-level rule selection (2LRS) and an appropriate learning of the membership function (MF) parameters to generate a set of Mamdani fuzzy rule-based systems with different trade-offs between accuracy and RB complexity. The 2LRS aims to select a reduced number of rules from a previously generated rule base and a reduced number of conditions for each selected rule. The learning adapts the cores of the MFs maintaining the partitions strong. The proposed approach has been experimented on two real world regression problems and the results have been compared with those obtained by applying the same multi-objective evolutionary algorithm for learning concurrently rules and MF parameters. We show that our approach achieves the best trade-offs between interpretability and accuracy.