Fuzzy System Modeling with the Genetic and Differential Evolutionary Optimization

This paper compares the performance of two provably successful evolutionary optimization tools in the optimization of a fuzzy-rule-base (FRB) for the three well known fuzzy modeling inference methods: Zadeh´s (center-of gravity), Kosko´s (standard-additive-model), and Takagi-Sugeno´s (local linear) model. In the fuzzy system modeling of an uncertain data, FRB keeps the model information within the fuzzy rules. The initial fuzzy-rule-base for the evolutionary optimization algorithms is extracted using Bezdek´s FCM. In the optimization, the normalized root mean square error of the training data is minimized for the fine-tuning of the FRB parameters for each of the inference models. The performance evaluation with the test cases indicates that differential evolutionary optimization achieves better results in terms of convergence speed and yields better parameters than the elitist genetic optimization