| Under the topic of management of uncertainty in expert systems using belief functions, we integrate two existing approaches described in earlier works by Kong and Shafer, Shenoy, and Mellouli.;One of the main results of this integration is the description of a propagation scheme for pooling evidence in qualitative Markov tree of the variables. This leads us to the problem of finding qualitative Markov tree representatives of a given hypergraph.;An ordering is defined on the set of all qualitative Markov tree representatives of a given hypergraph, and a method for constructing representatives is discussed. This method is shown to be optimal in the sense of its capability of producing optimal tree representatives.;We also study the relation between this work on qualitative Markov tree representatives and previous work on triangulation of graphs.;The search for an optimal tree remains an open question, but we show that by exploiting separation we can reduce the search for optimal trees to a smaller setting. |
