# Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models

arXiv: https://arxiv.org/abs/2202.08081 · HTML: https://mlsanity.com/paper/2202.08081/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 38 references that are in the map.
- First posted on arXiv 16 Feb 2022.

## Builds on (most cited first, 1 of 1)

- [Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence](https://mlsanity.com/paper/2004.11638/) (2020)

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

- [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)
- [Application of belief functions to medical image segmentation: A review](https://mlsanity.com/paper/2205.01733/) (2022)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [Evidential Fusion Network for Multimodal Survival Prediction under Missing Modalities](https://mlsanity.com/paper/2606.20757/) (2026)

## Abstract (arXiv)

We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random fuzzy sets are combined by the generalized product-intersection rule, which extends both Dempster's rule for combining belief functions, and the product conjunctive combination of possibility distributions. We introduce Gaussian random fuzzy numbers and their multi-dimensional extensions, Gaussian random fuzzy vectors, as practical models for quantifying uncertainty about scalar or vector quantities. Closed-form expressions for the combination, projection and vacuous extension of Gaussian random fuzzy numbers and vectors are derived.