A Multi-objective Genetic Approach to Concurrently Learn Partition Granularity and Rule Bases of Mamdani Fuzzy Systems

In this paper we propose a multi-objective genetic algorithm to generate Mamdani fuzzy rule-based systems with optimal trade-offs between complexity and accuracy. The main novelty of the algorithm is that both rule base and granularity of the uniform partitions defined on the input and output variables are learned concurrently. To this aim, we exploit a chromosome composed of two parts, which codify the numbers of fuzzy sets for each linguistic variable and the rule base, respectively. Rule bases defined on partitions with different granularity are handled by using an appropriate mapping strategy. The algorithm has been tested on a real word regression problem showing very promising results.