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Advances in Fuzzy Systems
Volume 2018, Article ID 5872195, 5 pages
Research Article

Why Are FGM Copulas Successful? A Simple Explanation

1Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand
2Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX 79968, USA

Correspondence should be addressed to Vladik Kreinovich; ude.petu@kidalv

Received 17 March 2017; Accepted 22 March 2018; Published 14 May 2018

Academic Editor: Katsuhiro Honda

Copyright © 2018 Songsak Sriboonchitta and Vladik Kreinovich. 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.


One of the most computationally convenient nonredundant ways to describe the dependence between two variables is by describing the corresponding copula. In many applications, a special class of copulas—known as FGM copulas—turned out to be most successful in describing the dependence between quantities. The main result of this paper is that these copulas are the fastest to compute, and this explains their empirical success. As an auxiliary result, we also show that a similar explanation can be given in terms of fuzzy logic.