# The intersection probability: betting with probability intervals

arXiv: https://arxiv.org/abs/2201.01729 · HTML: https://mlsanity.com/paper/2201.01729/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 118 references that are in the map.
- First posted on arXiv 5 Jan 2022.

## Builds on (most cited first, 8 of 8)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Visions of a generalized probability theory](https://mlsanity.com/paper/1810.10341/) (2018)
- [Decision under Uncertainty](https://mlsanity.com/paper/1304.1527/) (2013)
- [The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices](https://mlsanity.com/paper/1303.5408/) (2013)
- [A New Approach to Updating Beliefs](https://mlsanity.com/paper/1304.1119/) (2013)
- [The Nature of the Unnormalized Beliefs Encountered in the Transferable Belief Model](https://mlsanity.com/paper/1303.5430/) (2013)
- [Pignistic Probability Transforms for Mixes of Low- and High-Probability Events](https://mlsanity.com/paper/1505.07751/) (2015)
- [Theoretical Foundations for Abstraction-Based Probabilistic Planning](https://mlsanity.com/paper/1302.3581/) (2013)

## Built on by (most cited first, 6 of 6)

- [Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification](https://mlsanity.com/paper/2405.15047/) (2024)
- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [Credal Machine Learning for Risk-Averse Decision Making](https://mlsanity.com/paper/2610.12115/) (2026)

## Abstract (arXiv)

Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty, as the most natural such transformation. We recall its rationale and definition, compare it with other candidate representives of systems of probability intervals, discuss its credal rationale as focus of a pair of simplices in the probability simplex, and outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.