Identification of Mamdani Fuzzy Systems based on a Multi-Objective Genetic Algorithm

In this paper, we use a method based on a multi-objective genetic algorithm, namely the Pareto Archived Evolutionary Strategy (PAES), to generate a set of Mamdani fuzzy systems from numerical data. PAES determines an approximation of the optimal Pareto front by concurrently maximizing the accuracy and minimizing the complexity. Unlike other approaches, we measure the complexity as sum of the variables actually used in each rule, that is, as sum of the total number of conditions in the antecedents of the rules and of the number of consequents. Thus, low values of complexity correspond to Mamdani systems characterized by a low number of rules and a low number of input variables for each rule. This guarantees a high comprehensibility of the fuzzy rule base. Once the Pareto front has been generated, users can choose a posteriori the optimal Mamdani system for the specific domain. Results of the application of the method to two regression problems using the Miles per Gallons and the Box and Jenkins Gas Furnace datasets are shown and discussed