Fuzzy Vine Copula Construction: An Approach to Modeling Dependence Under Uncertainty

This paper introduces a systematic methodology for constructing vine copulas from fuzzy data, providing a novel framework for modeling complex dependence under uncertainty. Our approach first builds bivariate fuzzy copulas, including those from the Archimedean family, which serve as foundational building blocks. We then assemble these into a complete fuzzy vine structure. The methodology leverages the -cut decomposition of fuzzy numbers, transforming fuzzy parameters and data into intervals. This allows us to apply and extend standard copula techniques to interval-valued data, a key aspect of our contribution. The resulting framework addresses both parametric and structural uncertainties, opening new avenues for robust modeling in risk analysis, finance, engineering and other domains where uncertainty and dependence coexist.