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Mathematical Problems in Engineering
Volume 2013, Article ID 623757, 6 pages
Research Article

A New Distance Measure and Ranking Method for Generalized Trapezoidal Fuzzy Numbers

1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran

Received 28 January 2013; Accepted 13 April 2013

Academic Editor: Gozde Ulutagay

Copyright © 2013 T. Allahviranloo 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.


This study presents an approximate approach for ranking fuzzy numbers based on the centroid point of a fuzzy number and its area. The total approximate is determined by convex combining of fuzzy number’s relative and its area that is based on decision maker’s optimistic perspectives. The proposed approach is simple in terms of computational efforts and is efficient in ranking a large quantity of fuzzy numbers. A group of examples by Bortolan and Degani (1985) demonstrate the accuracy and applicability of the proposed approach. Finally by this approach, a new measure is introduced between two fuzzy numbers.