# Decision-Making with Belief Functions: a Review

arXiv: https://arxiv.org/abs/1808.05322 · HTML: https://mlsanity.com/paper/1808.05322/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2018.

## Built on by (most cited first, 13 of 13)

- [An evidential classifier based on Dempster-Shafer theory and deep learning](https://mlsanity.com/paper/2103.13549/) (2021)
- [Lymphoma segmentation from 3D PET-CT images using a deep evidential network](https://mlsanity.com/paper/2201.13078/) (2022)
- [Evidential fully convolutional network for semantic segmentation](https://mlsanity.com/paper/2103.13544/) (2021)
- [Application of belief functions to medical image segmentation: A review](https://mlsanity.com/paper/2205.01733/) (2022)
- [Partial-Label Learning with a Reject Option](https://mlsanity.com/paper/2402.00592/) (2024)
- [Fusion of evidential CNN classifiers for image classification](https://mlsanity.com/paper/2108.10233/) (2021)
- [Deep evidential fusion with uncertainty quantification and contextual discounting for multimodal medical image segmentation](https://mlsanity.com/paper/2309.05919/) (2023)
- [A geometric approach to conditioning belief functions](https://mlsanity.com/paper/2104.10651/) (2021)
- [A Distributional Approach for Soft Clustering Comparison and Evaluation](https://mlsanity.com/paper/2206.09827/) (2022)
- [Empirical Decision Theory](https://mlsanity.com/paper/2512.05677/) (2025)
- [The Geometry of Knowing: From Possibilistic Ignorance to Probabilistic Certainty -- A Measure-Theoretic Framework for Epistemic Convergence](https://mlsanity.com/paper/2604.09614/) (2026)
- [Decision-Aware Approximation of Belief Functions for Evidential Combinatorial Optimization](https://mlsanity.com/paper/2608.10650/) (2026)
- [Every pooling rule has its world: matching probability combination rules to situations and stakes](https://mlsanity.com/paper/2608.11275/) (2026)

## Abstract (arXiv)

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches.