Time-to-event analysis provides insights into clinical prognosis and treatment recommendations. However, this task is more challenging than standard regression problems due to the presence of censored observations. Additionally, the lack of confidence assessment, model robustness, and prediction calibration raises concerns about the reliability of predictions. To address these challenges, we propose an evidential regression model specifically designed for time-to-event prediction. The proposed model quantifies both epistemic and aleatory uncertainties using Gaussian Random Fuzzy Numbers and belief functions, providing clinicians with uncertainty-aware survival time predictions. The model is trained by minimizing a generalized negative log-likelihood function accounting for data censoring. Experimental evaluations using simulated datasets with different data distributions and censoring conditions, as well as real-world datasets across diverse clinical applications, demonstrate that our model delivers both accurate and reliable performance, outperforming state-of-the-art methods. These results highlight the potential of our approach for enhancing clinical decision-making in survival analysis.

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.

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.

The interpretation of unlabeled acoustic emission (AE) data classically relies on general-purpose clustering methods. While several external criteria have been used in the past to select the hyperparameters of those algorithms, few studies have paid attention to the development of dedicated objective functions in clustering methods able to cope with the specificities of AE data. We investigate how to explicitly represent clusters onsets in mixture models in general, and in Gaussian Mixture Models (GMM) in particular. By modifying the internal criterion of such models, we propose the first clustering method able to provide, through parameters estimated by an expectation-maximization procedure, information about when clusters occur (onsets), how they grow (kinetics) and their level of activation through time. This new objective function accommodates continuous timestamps of AE signals and, thus, their order of occurrence. The method, called GMMSEQ, is experimentally validated to characterize the loosening phenomenon in bolted structure under vibrations. A comparison with three standard clustering methods on raw streaming data from five experimental campaigns shows that GMMSEQ not only provides useful qualitative information about the timeline of clusters, but also shows better performance in terms of cluster characterization. In view of developing an open acoustic emission initiative and according to the FAIR principles, the datasets and the codes are made available to reproduce the research of this paper.

We propose an information-fusion approach based on belief functions to combine convolutional neural networks. In this approach, several pre-trained DS-based CNN architectures extract features from input images and convert them into mass functions on different frames of discernment. A fusion module then aggregates these mass functions using Dempster's rule. An end-to-end learning procedure allows us to fine-tune the overall architecture using a learning set with soft labels, which further improves the classification performance. The effectiveness of this approach is demonstrated experimentally using three benchmark databases.

The Gaussian mixture model (GMM) provides a convenient yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM), in the theoretical framework of belief functions to better characterize cluster-membership uncertainty. With a mass function representing the cluster membership of each object, the evidential Gaussian mixture distribution composed of the components over the powerset of the desired clusters is proposed to model the entire dataset. The parameters in EGMM are estimated by a specially designed Expectation-Maximization (EM) algorithm. A validity index allowing automatic determination of the proper number of clusters is also provided. The proposed EGMM is as convenient as the classical GMM, but can generate a more informative evidential partition for the considered dataset. Experiments with synthetic and real datasets demonstrate the good performance of the proposed method as compared with some other prototype-based and model-based clustering techniques.

Evidential clustering is an approach to clustering based on the use of Dempster-Shafer mass functions to represent cluster-membership uncertainty. In this paper, we introduce a neural-network based evidential clustering algorithm, called NN-EVCLUS, which learns a mapping from attribute vectors to mass functions, in such a way that more similar inputs are mapped to output mass functions with a lower degree of conflict. The neural network can be paired with a one-class support vector machine to make it robust to outliers and allow for novelty detection. The network is trained to minimize the discrepancy between dissimilarities and degrees of conflict for all or some object pairs. Additional terms can be added to the loss function to account for pairwise constraints or labeled data, which can also be used to adapt the metric. Comparative experiments show the superiority of N-EVCLUS over state-of-the-art evidential clustering algorithms for a range of unsupervised and constrained clustering tasks involving both attribute and dissimilarity data.

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches.

We revisit logistic regression and its nonlinear extensions, including multilayer feedforward neural networks, by showing that these classifiers can be viewed as converting input or higher-level features into Dempster-Shafer mass functions and aggregating them by Dempster's rule of combination. The probabilistic outputs of these classifiers are the normalized plausibilities corresponding to the underlying combined mass function. This mass function is more informative than the output probability distribution. In particular, it makes it possible to distinguish between lack of evidence (when none of the features provides discriminant information) from conflicting evidence (when different features support different classes). This expressivity of mass functions allows us to gain insight into the role played by each input feature in logistic regression, and to interpret hidden unit outputs in multilayer neural networks. It also makes it possible to use alternative decision rules, such as interval dominance, which select a set of classes when the available evidence does not unambiguously point to a single class, thus trading reduced error rate for higher imprecision.