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Mathematical Problems in Engineering
Volume 2013, Article ID 452780, 16 pages
http://dx.doi.org/10.1155/2013/452780
Research Article

Uncertainty in Interval Type-2 Fuzzy Systems

School of Electrical and Electronics Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Pulau Pinang, Malaysia

Received 8 June 2013; Accepted 1 August 2013

Academic Editor: Alexander P. Seyranian

Copyright © 2013 Sadegh Aminifar and Arjuna Marzuki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies uncertainty and its effect on system response displacement. The paper also describes how IT2MFs (interval type-2 membership functions) differentiate from T1MFs (type-1 membership functions) by adding uncertainty. The effect of uncertainty is modeled clearly by introducing a technique that describes how uncertainty causes membership degree reduction and changing the fuzzy word meanings in fuzzy logic controllers (FLCs). Several criteria are discussed for the measurement of the imbalance rate of internal uncertainty and its effect on system behavior. Uncertainty removal is introduced to observe the effect of uncertainty on the output. The theorem of uncertainty avoidance is presented for describing the role of uncertainty in interval type-2 fuzzy systems (IT2FSs). Another objective of this paper is to derive a novel uncertainty measure for IT2MFs with lower complexity and clearer presentation. Finally, for proving the affectivity of novel interpretation of uncertainty in IT2FSs, several investigations are done.