Defining new approximations of belief function by means of Dempster's combination

Approximating a belief function (with a probability distribution or with another belief function with a restricted number of focal elements) is an important issue in Dempster-Shafer Theory. The reason is that such approximations are really useful in two different situations: (1) decision making and (2) computational saving. In this paper, we propose to consider the definition of a proxy for a belief function as the result of the Dempster's combination of two belief functions: The first one is the belief function to approximate and the second one is a Bayesian belief function which encodes a meta-information describing the support of the approximation (i.e. the set of the potential focal elements of the proxy).