Type-2 Fuzzy Set Theory and its Application to a Dynamical System with Noise
Abstract
In this article, type-2 fuzzy sets, as extensions of the ordinary or type-1 fuzzy sets, are considered. Originally, type-2 fuzzy sets were utilized to represent the uncertainties about the membership function grades themselves. After summarizing some preliminary type-2 fuzzy set concepts, a possible extension of the type-1 fuzzy inference engine is presented. Utilizing this extension, the identification of a dynamical system, specifically the inverted pendulum on a cart, under noisy conditions is considered. The applicability of type-2 fuzzy sets on the identification of dynamical systems is demonstrated. The cases when effects of the noise are poorly handled by the type-1 fuzzy sets were shown to be well handled by type-2 fuzzy sets.
This paper has been withdrawn.
