A genetic method for designing TSK models based on objective weighting: application to classification problems.

Abstract

This paper proposes a genetic-based algorithm for generating simple and well-defined Takagi-Sugeno-Kang (TSK) models. The method handles several attributes simultaneously, such as the input partition, feature selection and estimation of the consequent parameters. The model building process comprises three stages. In stage one, structure learning is formulated as an objective weighting optimization problem. Apart from the mean square error (MSE) and the number of rules, three additional criteria are introduced in the fitness function for measuring the quality of the partitions. Optimization of these measures leads to models with representative rules, small overlapping and efficient data cover. To obtain models with good local interpretation, the consequent parameters are determined using a local MSE function while the overall model is evaluated on the basis of a global MSE function. The initial model is simplified at stage two using a rule base simplification routine. Similar fuzzy sets are merged and the “don’t care” premises are recognized. Finally, the simplified models are fine-tuned at stage three to improve the model performance. The suggested method is used to generate TSK models with crisp and polynomial consequents for two benchmark classification problems, the iris and the wine data. Simulation results reveal the effectiveness of our method. The resulting models exhibit simple structure, interpretability and superior recognition rates compared to other methods of the literature.