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Journal of Applied Mathematics
Volume 2014, Article ID 254853, 22 pages
http://dx.doi.org/10.1155/2014/254853
Research Article

The Interval-Valued Trapezoidal Approximation of Interval-Valued Fuzzy Numbers and Its Application in Fuzzy Risk Analysis

1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Received 27 February 2014; Revised 27 May 2014; Accepted 9 July 2014; Published 12 August 2014

Academic Editor: Francisco J. Marcellán

Copyright © 2014 Zengtai Gong and Shexiang Hai. 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

Taking into account that interval-valued fuzzy numbers can provide more flexibility to represent the imprecise information and interval-valued trapezoidal fuzzy numbers are widely used in practice, this paper devotes to seek an approximation operator that produces an interval-valued trapezoidal fuzzy number which is the nearest one to the given interval-valued fuzzy number, and the approximation operator preserves the core of the original interval-valued fuzzy number with respect to the weighted distance. As an application, we use the interval-valued trapezoidal approximation to handle fuzzy risk analysis problems, which overcome the drawback of existing fuzzy risk analysis methods.