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Mathematical Problems in Engineering
Volume 2013, Article ID 424186, 4 pages
http://dx.doi.org/10.1155/2013/424186
Research Article

A New Distance Measure for Trapezoidal Fuzzy Numbers

1Faculty of Marine Science, Chabahar Maritime University, Chabahar, Iran
2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
4Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran
5Young Researchers and Elite Club, Islamic Azad University, Mobarakeh Branch, Mobarakeh, Iran

Received 6 February 2013; Accepted 25 March 2013

Academic Editor: Tofigh Allahviranloo

Copyright © 2013 M. J. Ebadi 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.

Abstract

We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and left/right spread of trapezoidal fuzzy numbers. Moreover, the metric properties of suggested distance measure are investigated. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right spreads go to zero, then two given fuzzy numbers are equal. Consequently, we complete discussion about the relation between fuzzy number and its centroid which is the firstly discussed by Hadi-Vencheh and Allame (2010). To the best of our knowledge, this is first time in the literature that such metric is applied by centroid point.