Additivity of uncertainty measures on credal sets

A general way of representing incomplete information is to use closed and convex sets of probability distributions, which are also called credal sets. Each credal set is associated with uncertainty, whose amount is quantified by an appropriate uncertainty measure. One of the requisite properties of uncertainty measures is the property of additivity, which is associated with the concept of independence. For credal sets, the concept of independence is not unique. This means that different definitions of independence lead to different definitions of additivity for uncertainty measures. In this paper, we compare the various definitions of independence, but our principal aim is to analyze those definitions that are employed in the most significant uncertainty measures established in the literature for credal sets.