Exploiting a three-objective evolutionary algorithm for generating Mamdani fuzzy rule-based systems

In this paper, we propose a three-objective evolutionary algorithm to generate a set of Mamdani fuzzy rule-based systems (MFRBSs) with different tradeoffs between accuracy, rule base (RB) complexity and partition integrity. The RB, the linguistic partition granularities and the membership function (MF) parameters are concurrently learnt during the evolutionary process. In particular, the granularity learning is performed by exploiting the concept of virtual RB and an appropriate mapping strategy, and the MF parameter tuning is achieved by a piecewise linear transformation. The RB complexity is measured as the total number of conditions in the antecedents of the rules and the partition integrity is evaluated by using a purposely-defined index, based on the piecewise linear transformation. We use a chromosome composed of three parts, which codify, respectively, the RB, and, for each variable, the number of fuzzy sets and the parameters of the piecewise linear transformation of the membership functions. Results on two real-world regression problems are shown and discussed.