Using the transformed data to construct an extension-based fuzzy inference model

Adjusting the membership functions to satisfy one pattern may deteriorate the inference outcomes of the others. This incompatible issue can be retarded by the extension theory. A novel extension-based fuzzy modeling method, which differs from the traditional fuzzy inference, is proposed. Instead of directly applying the given data to building the fuzzy model, the given data are transformed to another domain by a sigmoidal function to obtain a better fuzzy model. We also define the extended correlation functions to relate the data with the fuzzy sets. During the refining process, the extended fuzzy model, which considers the positive and negative sets simultaneously, is adjusted by the gradient descent method. Simulation results from both single-input-single-output and double-input-single-output systems verified that better results than the conventional methods can be obtained