An Interval Type-2 Fuzzy Dependence Framework for Sensitivity Analysis of R-Vine Copula Models

This paper proposes a novel Interval Type-2 fuzzy linguistic framework for assessing the interpretability and linguistic-partition sensitivity of R-vine copula dependence analysis. Kendall’s rank correlation coefficients obtained from the estimated pair-copulas are transformed into linguistic dependence categories using triangular fuzzy membership functions and aggregated into a Fuzzy Dependence Score (FDS). To account for uncertainty in the linguistic partition, the proposed methodology extends the Type-1 fuzzy model to Interval Type-2 fuzzy sets and employs the Karnik–Mendel type-reduction algorithm to compute an Interval Type-2 Fuzzy Dependence Score (IT2-FDS). The framework is illustrated using technology stocks, Bitcoin, gold, and crude oil. The results reveal heterogeneous dependence patterns and show that the proposed Interval Type-2 extension preserves the dependence ranking while quantifying sensitivity to linguistic-partition uncertainty in the fuzzy category definitions. An extended validation on a ten-asset universe across three non-overlapping subperiods and a grid of uncertainty widths shows that the ranking is stable within the tested perturbation range but not across all regimes. Robustness here means sensitivity to the linguistic-partition width only, not to sampling, model-selection, or parameter uncertainty. No improvement over a Type-1 alternative is claimed, and rank agreement reflects the numerically verified monotonicity of the scoring transformation.