# Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence

arXiv: https://arxiv.org/abs/2004.11638 · HTML: https://mlsanity.com/paper/2004.11638/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2020.

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

- [Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models](https://mlsanity.com/paper/2202.08081/) (2022)
- [An Evidential Neural Network Model for Regression Based on Random Fuzzy Numbers](https://mlsanity.com/paper/2208.00647/) (2022)
- [DPsurv: Dual-Prototype Evidential Fusion for Uncertainty-Aware and Interpretable Whole-Slide Image Survival Prediction](https://mlsanity.com/paper/2510.00053/) (2025)
- [An evidential time-to-event prediction model based on Gaussian random fuzzy numbers](https://mlsanity.com/paper/2406.13487/) (2024)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [Belief functions on ordered frames of discernment](https://mlsanity.com/paper/2210.04535/) (2022)

## Abstract (arXiv)

We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, and show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.