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Mathematical Problems in Engineering
Volume 2013, Article ID 824706, 10 pages
Research Article

A New Similarity Measure of Generalized Trapezoidal Fuzzy Numbers and Its Application on Rotor Fault Diagnosis

Department of Automation, China University of Petroleum-Beijing (CUPB), Beijing 102249, China

Received 8 January 2013; Accepted 24 January 2013

Academic Editor: Valentina E. Balas

Copyright © 2013 Xin Zuo et al. 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.


Fault diagnosis technology plays a vital role in the variety of critical engineering applications. Fuzzy approach is widely employed to cope with decision-making problems because it is in the simplest and most used form. This paper proposed a new similarity measure of generalized trapezoidal fuzzy numbers used for fault diagnosis. The presented similarity measure combines concepts of the geometric distance, the center of gravity point, the perimeter, and the area of the generalized trapezoidal fuzzy numbers for calculating the degree of similarity between generalized trapezoidal fuzzy numbers. This method is proposed to deal with both standardized and nonstandardized generalized trapezoidal fuzzy numbers. Some properties of the proposed similarity measure have been proved, and 12 sets of generalized fuzzy numbers have been used to compare the calculation results of the proposed similarity measures with the existing similarity measures. Comparison results indicate that the proposed similarity measure can overcome the drawbacks of existing similarity measures. Finally, a fault diagnosis experiment is carried out in laboratory based on multifunctional flexible rotor experiment bench. Experimental results demonstrate that the proposed similarity measure is more effective than other methods in terms of rotor fault diagnosis.