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

TL;DR

This paper introduces a flexible belief model that combines Dempster-Shafer Theory and Topological Models to handle inconsistent and uncertain evidence, enabling tailored belief computations for decision-making.

Contribution

It presents a novel, general belief model that can reproduce existing approaches and adapt to different evidential demands, addressing challenges in evidence fusion.

Findings

The model can reproduce existing belief approaches.

It allows computation of beliefs based on different evidential priorities.

Belief computation with the model is #P-complete in general.

Abstract

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.