  One problem to solve in the context of information fusion, decision-making,
and other artificial intelligence challenges is to compute justified beliefs
based on evidence. In real-life examples, this evidence may be inconsistent,
incomplete, or uncertain, making the problem of evidence fusion highly
non-trivial. In this paper, we propose a new model for measuring degrees of
beliefs based on possibly inconsistent, incomplete, and uncertain evidence, by
combining tools from Dempster-Shafer Theory and Topological Models of Evidence.
Our belief model is more general than the aforementioned approaches in two
important ways: (1) it can reproduce them when appropriate constraints are
imposed, and, more notably, (2) it is flexible enough to compute beliefs
according to various standards that represent agents' evidential demands. The
latter novelty allows the users of our model to employ it to compute an agent's
(possibly) distinct degrees of belief, based on the same evidence, in
situations when, e.g, the agent prioritizes avoiding false negatives and when
it prioritizes avoiding false positives. Finally, we show that computing
degrees of belief with this model is #P-complete in general.
