Analytical Construction and Theoretical Properties of Fuzzy Archimedean and Elliptical Copulas

A. In this article, we propose an approach to modeling uncertain dependence through the construction of fuzzy copulas.We develop fuzzy Archimedean copulas (Clayton and Frank), fuzzy elliptical copulas (Gaussian), and a fuzzy extreme value copula (Gumbel).A comparative analysis with their classical counterparts is conducted.Finally, we introduce fuzzy association measures, such as fuzzy tau of Kendall based on fuzzy generator functions, to better represent the uncertainty present in the data.