Maxitive Belief Structures and Imprecise Possibility Distributions

We introduce the idea of maxitive belief structures, MBS, as a framework for modeling imprecise possibility distributions in a manner analogous to the way Dempster-Shafer belief structures allows the modeling of imprecise probability distributions. We study various properties of these MBS. We consider the problem of obtaining possibility distributions compatible with these belief structures. We consider the problem of fusing multiple MBS and the performance of various arithmetic operations with these objects.