The designing methodology of extenics-based fuzzy reasoning model

A novel extenics-based fuzzy modeling method, which differs from the traditional fuzzy inference, is proposed. In the parameter identification process, adjusting a membership function to satisfy one pattern may deteriorate the others' performance and result in a lengthy tuning process. This incompatible issue is solved by extension theory. We investigate how to define the extended relational functions and how to refine the roughly designed model to meet the system requirement. During the refining process, both the fired and the neighborhood of the fired membership functions are adjusted. On the basis of the gradient descent method, the parameters used to define the extended relational functions and fuzzy rules can be systematically adjusted. We also use the transformation technique to simplify fuzzy modeling. Simulation results from models of single-input single-output, double-input single-output and sigmoidal transformation functions verified that better results than the conventional methods have been obtained.