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.

翻译：在信息融合、决策及其他人工智能挑战的背景下，需解决的核心问题之一是基于证据计算合理的信念。现实中的证据可能不一致、不完整或不确定，这使得证据融合问题高度复杂。本文通过结合登普斯特-沙夫理论与证据拓扑学模型，提出了一种基于可能不一致、不完整且不确定的证据测量信念度的新模型。我们的信念模型在以下两个重要方面比前述方法更具通用性：（1）在施加适当约束时可复现这些方法；（2）更关键的是，它足够灵活，能够根据代表智能体证据需求的不同标准计算信念。后者的创新性允许用户基于相同证据，在智能体优先避免假阴性或优先避免假阳性等情境下，计算其（可能的）不同信念度。最后，我们证明使用该模型计算信念度在一般情况下是#P完全的。