Type-2 Fuzzy Set Theory and its Application to a Dynamical System with Noise


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.

Meeting Name

1999 Artificial Neural Networks in Engineering Conference, ANNIE '99 (1999: Nov. 7-10, St. Louis, MO)


Electrical and Computer Engineering

Keywords and Phrases

Fuzzy sets; Inference engines; Membership functions; Probability; Spurious signal noise; Inverted pendulum; Neural networks

International Standard Book Number (ISBN)

9780791800980; 0791800989

Document Type

Article - Conference proceedings

Document Version


File Type





© 1999 American Society of Mechanical Engineers (ASME), All rights reserved.

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