# An Evidential Neural Network Model for Regression Based on Random Fuzzy Numbers

arXiv: https://arxiv.org/abs/2208.00647 · HTML: https://mlsanity.com/paper/2208.00647/

## Key facts

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

## Builds on (most cited first, 6 of 6)

- [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)
- [Valid inferential models for prediction in supervised learning problems](https://mlsanity.com/paper/2112.10234/) (2021)
- [Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence](https://mlsanity.com/paper/2004.11638/) (2020)
- [Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models](https://mlsanity.com/paper/2202.08081/) (2022)

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

- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Random-Set Neural Networks (RS-NN)](https://mlsanity.com/paper/2307.05772/) (2023)
- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [Credal and Interval Deep Evidential Classifications](https://mlsanity.com/paper/2512.05526/) (2025)
- [An evidential time-to-event prediction model based on Gaussian random fuzzy numbers](https://mlsanity.com/paper/2406.13487/) (2024)
- [Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluation](https://mlsanity.com/paper/2512.23753/) (2025)

## Abstract (arXiv)

We introduce a distance-based neural network model for regression, in which prediction uncertainty is quantified by a belief function on the real line. The model interprets the distances of the input vector to prototypes as pieces of evidence represented by Gaussian random fuzzy numbers (GRFN's) and combined by the generalized product intersection rule, an operator that extends Dempster's rule to random fuzzy sets. The network output is a GRFN that can be summarized by three numbers characterizing the most plausible predicted value, variability around this value, and epistemic uncertainty. Experiments with real datasets demonstrate the very good performance of the method as compared to state-of-the-art evidential and statistical learning algorithms. keywordsEvidence theory, Dempster-Shafer theory, belief functions, machine learning, random fuzzy sets.