Uncertainty Measures in Evidence Theory: A Genealogy

We consider the problem of quantification of uncertainty in the framework of evidence theory. A large number of uncertainty measures have been proposed in the last 40 years to perform this task, and contributions, albeit numerous, are scattered in the literature, and it is difficult to have an idea of how many measures exist, let alone to know their formal definitions and their evolution in time. In this article, we provide a self-contained exposition of 65 uncertainty measures—out of which 43 were proposed in the last decade—and then we consider their development from the temporal point of view, as well as the lineage of each one from previous ones. These two analyses help us see that 2016 was an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">annus mirabilis</i>, since the three measures proposed in that year would later on become extremely influential. Moreover, our analysis offers at least three insights that may hopefully open the floor for future research. First, the recent proliferation of uncertainty measures has not always been accompanied by sufficiently deep analyses on their formal properties. Second, the widely accepted behavioral requirement that the total uncertainty must be the sum of the contributions of non-specificity and conflict appears questionable in light of its necessary conditions. Third, and last, the choice of the most suitable measure cannot be detached from the interpretation that is given to the belief function.