The extension-based fuzzy modeling method and its applications

The newly developed extension theory and conventional gradient descent method are applied to adjusting a fuzzy model to satisfy the given data. In the commonly used fuzzy model, a fuzzy rule or the corresponding membership function is refined when the rule or the fuzzy set is mapped by a data pattern. To take the neighborhood of the given data point into account during the refining process, an extension-based fuzzy model is proposed. We also investigate how to define the extended relational function such that the designed system can accommodate the well-known fuzzy model. On the basis of gradient descent method, the parameters used to define the extended relational functions and fuzzy rules can be systematically adjusted. The proposed models are shown to have a better performance than the conventional methods. Simulation results from two different examples verify the effectiveness and applicability of the proposed work.