Cooperative Evolutionary Learning of Linguistic Fuzzy Rules and Parametric Aggregation Connectors for Mamdani Fuzzy Systems

There are two tasks in the design of linguistic fuzzy models for a concrete application: The derivation of the linguistic rule base and the setup of the inference system and the defuzzification method. Traditionally, the derivation of the linguistic rule base has been considered the most important task, but the use of the appropriate aggregation connectors in the inference system and the defuzzification interface can improve the fuzzy system behavior. In this paper, we take in consideration this idea, we propose an evolutionary learning method to learn a linguistic rule base and the parametric aggregation connectors of the inference and defuzzification in a single step. The aim of this methodology is to make possible a high level of positive synergy between the linguistic rule base and the aggregation connectors, improving the accuracy of the linguistic Mamdani fuzzy systems. Our proposal has shown good results solving three different applications. We introduce a statistical analysis of results for validating the model behavior on the applications used in the experimental study. We must remark that we present an experimental study with a double intention: (a) to compare the behavior of the new approach in comparison with those ones that first learn the rule base and then adapt the connectors, and (b) to analyze the rule bases obtained with fixed aggregation connectors and with the adaptive ones for showing the changes on the consequent rules, changes on labels that produce a better behavior of the linguistic model than the classic ones.