# Belief functions on ordered frames of discernment

arXiv: https://arxiv.org/abs/2210.04535 · HTML: https://mlsanity.com/paper/2210.04535/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 15 references that are in the map.
- First posted on arXiv 10 Oct 2022.

## Builds on (most cited first, 5 of 5)

- [Decision under Uncertainty](https://mlsanity.com/paper/1304.1527/) (2013)
- [Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence](https://mlsanity.com/paper/2004.11638/) (2020)
- [Conflict management in information fusion with belief functions](https://mlsanity.com/paper/1709.04182/) (2017)
- [Fuzzy Jaccard Index: A robust comparison of ordered lists](https://mlsanity.com/paper/2008.02216/) (2020)
- [A Distance-Based Decision in the Credal Level](https://mlsanity.com/paper/1501.07008/) (2015)

## Abstract (arXiv)

Most questionnaires offer ordered responses whose order is poorly studied via belief functions. In this paper, we study the consequences of a frame of discernment consisting of ordered elements on belief functions. This leads us to redefine the power space and the union of ordered elements for the disjunctive combination. We also study distances on ordered elements and their use. In particular, from a membership function, we redefine the cardinality of the intersection of ordered elements, considering them fuzzy.