A numerical comparative study of uncertainty measures in the Dempster-Shafer evidence theory

We consider a wide range of measures of uncertainty that have been proposed within the Dempster-Shafer evidence theory. All these measures aim to quantify the uncertainty associated with a given basic probability assignment. As a preliminary step, we offer a study of the literature, which shows a recent resurgence of interest in the quantification of uncertainty in the evidence theory. Then, we compare a number of uncertainty measures by means of numerical simulations and analyze their similarities and differences using rank correlation coefficients, hierarchical clustering, and centrality analysis. The results show that uncertainty measures with similar formulations do not necessarily have similar numerical properties, and some original results are obtained. In particular, we demonstrate that numerical studies on uncertainty measures are necessary to obtain more insight and to enhance the interpretability of the values returned by the measures.