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One problem to solve in the context of information fusion, decision-making,and other artificial intelligence challenges is to compute justified beliefsbased on evidence. In real-life examples, this evidence may be inconsistent,incomplete, or uncertain, making the problem of evidence fusion highlynon-trivial. In this paper, we propose a new model for measuring degrees ofbeliefs based on possibly inconsistent, incomplete, and uncertain evidence, bycombining tools from Dempster-Shafer Theory and Topological Models of Evidence.Our belief model is more general than the aforementioned approaches in twoimportant ways: (1) it can reproduce them when appropriate constraints areimposed, and, more notably, (2) it is flexible enough to compute beliefsaccording to various standards that represent agents' evidential demands. Thelatter 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, insituations when, e.g, the agent prioritizes avoiding false negatives and whenit prioritizes avoiding false positives. Finally, we show that computingdegrees of belief with this model is #P-complete in general.

A Belief Model for Conflicting and Uncertain Evidence -- Connecting Dempster-Shafer Theory and the Topology of Evidence