Addressing class imbalance is a prevalent challenge in image classification tasks, where the minority class often carries higher importance and misclassifying its samples can be particularly costly. Oversampling (data augmentation) is one of the most effective strategies to mitigate this issue. In parallel, accounting for predictive uncertainty becomes crucial when class imbalance is coupled with ambiguity, such as class overlap, noisy labels, or visually borderline samples. In this paper, we introduce a novel framework that combines generative adversarial networks (GANs) and evidence theory to explicitly generate high-uncertainty minority images. Evidential information is leveraged as auxiliary guidance and incorporated into the GAN training scheme through a new regularization term, referred to as evidential loss. The primary objective is to guide the generative model toward creating ambiguous boundary minority images, thereby strengthening the minority decision boundary and improving classifier robustness. We propose a joint training scheme that alternates the optimization of the evidential network and the GAN, so that uncertainty estimation and generation improve each other during training. We evaluate our approach on image datasets, including MNIST handwritten digits and two medical benchmarks (OCTMNIST and DermaMNIST), and we show consistent improvements over standard conditional GAN-based augmentation baselines.

This paper deals with an inter-turn short-circuit fault detection approach for synchronous machines using timedomain analysis of the external magnetic field. We compare single-sensor and dual-sensor configurations, extracting 22 timeseries features using the Catch22 algorithm to classify healthy and faulty states. Machine learning classifiers are employed; they are initially trained on simulated data and later refined using a mixed dataset incorporating experimental signals to improve generalization. Results show that logistic regression struggles with nonlinear patterns, while random forest demonstrates superior robustness. The dual-sensor configuration further enhances detection, confirming it as the most effective strategy for accurate and reliable fault classification.

Real-world Vehicle Routing Problems (VRPs) involve multiple operational attributes such as capacity limits, time windows, backhauls, open routes, and route duration constraints. Most existing methods are tailored to specific variants, limiting adaptability and reuse. This paper introduces G-UniRouting: $A$ Graph-Based Unified Neural Model for Solving Multi-Attribute Vehicle Routing Problems. Our approach integrates a Graph Neural Network (GNN) encoder that captures spatial and relational structure with a constraint-aware decoder that dynamically enforces feasibility through dynamic masking and distance-aware attention mechanisms. Our proposed model is an end-to-end framework trained using the REINFORCE algorithm with a rollout baseline to minimize routing costs. G-UniRouting is evaluated on 24 distinct VRP variants within a unified framework and employs multi-start inference to enhance solution quality. Experimental results show that our unified model generalizes across diverse constraints and consistently outperforms or rivals specialized baselines, offering a scalable and flexible solution to complex, multi-attribute routing problems.

We study a general optimization problem in which coefficients in the objective are uncertain. We use capacities (lower probabilities) to model such uncertainty. Two popular criteria in imprecise probability, namely maximality and E-admissibility, are employed to compare solutions. We characterize non-dominated solutions with respect to these criteria in terms of well-known notions in multi-objective optimization. These characterizations are novel and make it possible to derive several interesting results. Specially, for convex problems, maximality and E-admissibility are equivalent for any capacities even though the set of associated acts is not convex, and in case of 2-monotone capacities, finding an arbitrary non-dominated solution and checking if a given solution is non-dominated are both tractable. For combinatorial problems, we show a general result: in case of 2-monotone capacities, if the deterministic version of the problem can be solved in polynomial time, checking E-admissibility can also be done in polynomial time. Lastly, for the matroid optimization problem, more refined results are also obtained thanks to these characterizations, namely the connectedness of E-admissible solutions and an outer approximation based on the greedy algorithm for non-dominated solutions with respect to maximality.

We study a general optimization problem with an uncertain linear objective. We address the uncertainty using two models: belief functions and, more generally, capacities. In the former model, we use the generalized minimax regret criterion introduced by Yager, while in the latter one, we extend this criterion, to find optimal solutions. This paper identifies some tractable cases for the resulting problem. Furthermore, when focal sets of the considered belief functions are Cartesian products of intervals, we develop a 2-approximation method that mirrors the well-known midpoint scenario method used for minimax regret optimization problems with interval data.

Imbalanced classification refers to problems in which there are significantly more instances available for some classes than for others. Such scenarios require special attention because traditional classifiers tend to be biased towards the majority class which has a large number of examples. Different strategies, such as re-sampling, have been suggested to improve imbalanced learning. Ensemble methods have also been proven to yield promising results in the presence of class-imbalance. However, most of them only deal with binary imbalanced datasets. In this paper, we propose a re-sampling approach based on belief function theory and ensemble learning for dealing with class imbalance in the multi-class setting. This technique assigns soft evidential labels to each instance. This evidential modeling provides more information about each object's region, which improves the selection of objects in both undersampling and oversampling. Our approach firstly selects ambiguous majority instances for undersampling, then oversamples minority objects through the generation of synthetic examples in borderline regions to better improve minority class borders. Finally, to improve the induced results, the proposed re-sampling approach is incorporated into an evidential classifier-independent fusion-based ensemble. The comparative study against well-known ensemble methods reveals that our method is efficient according to the G-Mean and F1-score measures, independently from the chosen classifier.

Recent works have studied 0-1 combinatorial optimization problems where profits of items are measured on a qualitative scale such as “low”, “medium” and “high”. In this study, we extend this body of work by allowing these profits to be both qualitative and uncertain. In the first step, we use probability theory to handle uncertainty. In the second step, we use evidence theory to handle uncertainty. We combine their approaches with approaches in decision making under uncertainty that utilize the Maximum Expected Utility principle and generalized Hurwicz criterion, to compare solutions. We show that under probabilistic uncertainty and a special case of evidential uncertainty where the focal sets are rectangles, the task of identifying the non-dominated solutions can be framed as solving a multi-objective version of the considered problem. This result mirrors that of the case of qualitative profits with no uncertainty.

Ensemble classifier is a well-known method that has been used to solve several machine learning problems. To have reliable results, one should ensure the build of a good ensemble. In order to do so, researchers have proposed some heuristics like Random Subspace Ensemble (RSM), Rough set bas. The drawback of these mentioned approaches is their disability to handle uncertain data especially when uncertainty is represented by the evidence theory. The aim of this paper is to adapt both RSM and Rough set based ensemble in order to let them working in the context of evidential data. Three ensemble classifier approaches based on the rough set theory have been proposed and have been compared with each other. For the comparison purpose, we have relied on Ensemble Enhanced Evidential k Nearest Neighbor (EEk-NN) classifier, real world datasets from the UCI repository as well as synthetic databases.

The predictive performance of machine learning models tends to deteriorate in the presence of class imbalance. Multiple strategies have been proposed to address this issue. A popular strategy consists of oversampling the minority class. Classic approaches such as SMOTE utilize techniques like nearest neighbor search and linear interpolation, which can pose difficulties when dealing with datasets that have a large number of dimensions and intricate data distributions. As a way to create synthetic examples in the minority class, Generative Adversarial Networks (GANs) have been suggested as an alternative technique due to their ability to simulate complex data distributions. However, most GAN-based oversampling methods tend to ignore data uncertainty. In this paper, we propose a novel GAN-based oversampling method using evidence theory. An auxiliary evidential classifier is incorporated in the GAN architecture in order to guide the training process of the generative model. The objective is to push GAN to generate minority objects at the borderline of the minority class, near difficult-to-classify objects. Through extensive analysis, we demonstrate that the proposed approach provides better performance, compared to other popular methods.

We investigate a general optimization problem with a linear objective in which the coefficients are uncertain and the uncertainty is represented by a belief function. We consider five common criteria to compare solutions in this setting: generalized Hurwicz, strong dominance, weak dominance, maximality and E-admissibility. We provide characterizations for the non-dominated solutions with respect to these criteria when the focal sets of the belief function are Cartesian products of compact sets. These characterizations correspond to established concepts in optimization. They make it possible to find non-dominated solutions by solving known variants of the deterministic version of the optimization problem or even, in some cases, simply by solving the deterministic version.

In many real-world binary classification problems, one class tends to be heavily underrepresented when it consists of far fewer observations than the other class. This results in creating a biased model with undesirable performance. Different techniques, such as undersampling, have been proposed to fix this issue. Ensemble methods have also been proven to be a good strategy to improve the performance of the resulting model in the case of class imbalance. In this paper, we propose an evidential undersampling-based ensemble approach. To alleviate the issue of losing important data, our undersampling technique assigns soft evidential labels to each majority instance, which are later used to discard only the unwanted observations, such as noisy and ambiguous examples. Finally, to improve the final results, the proposed undersampling approach is incorporated into an evidential classifier fusion-based ensemble. The comparative study against well-known ensemble methods reveal that our method is efficient according to the G-Mean and F-Score measures.

Learning from class-imbalanced datasets has gained substantial attention in the machine learning community, leading to solutions for healthcare, security, banking, etc. Specifically, binary imbalanced problems has received the most interest in the field. Yet, there has been little emphasis given to dealing with multi-class imbalance learning. Data imbalance can significantly worsen the classification performance, especially in the presence of other data difficulties such as uncertainty, i.e., ambiguous samples and noise. In this paper, we present an evidential hybrid re-sampling method for dealing with class imbalance in the multi-class setting. This technique uses the evidence theory to assign a soft label to each object. This evidential modeling provides more information about each object’s region, which improves the selection of objects in both undersampling and oversampling. Our approach firstly selects ambiguous majority instances for undersampling, then oversamples minority objects through the generation of synthetic examples in borderline regions to better improve minority class borders. An adjustment has also been integrated in order to avoid excessive oversampling and undersampling. Benchmarking results have shown significant improvement of G-Mean of AUC metrics over other popular re-sampling methods.

We study the single source single destination shortest path problem in a graph where information about arc weights is modelled by a belief function. We consider three common criteria to compare paths with respect to their weights in this setting: generalized Hurwicz, strong dominance and weak dominance. We show that in the particular case where the focal sets of the belief function are Cartesian products of intervals, finding best, i.e. , non-dominated, paths according to these criteria amounts to solving known variants of the deterministic shortest path problem, for which exact resolution algorithms exist.

The online success of the brands, products or services depends upon the online reviews written by the consumers to share their experiences. These reviews deeply affect the buying decision of the new customers. For the purpose of performing their e-reputation, some companies rely on spammers to involve fraud reviews with the aim of gaining more profit. They can work individually or collaborate together to post various fake reviews trying to promote or demote target companies or products. These spammers and the group of spammers mislead the readers which make the e-commerce unsafe domain. To deal with this issue, we propose a new method having the objective to detect the spammers while taking into account both the group spammers and the individual spammers indicators. Our proposed method relies on the K-nearest neighbors algorithm under the belief function theory in order to handle the uncertainty in both the spammers and the group spammers indicators. Experiments are conducted on two labeled real datasets extracted from Yelp.com where our method achieves significant results.

Adopting a general framework to faithfully represent uncertainty, such as belief function theory, usually comes at a cost. In many real-life applications, we are constrained to handle mass functions that have too many focal elements. Fortunately, one can resort to approximation techniques to bypass this issue. In this paper, we extend the classical approximation techniques, which are mainly specificity-based, to other belief function relations such as lattice dominance. This allows to overcome the limits of classical techniques in some applications.

This paper addresses a variant of the vehicle routing problem with time windows where service and travel times are modeled within the framework of belief function theory. This theory is general as it offers to model several facets of information imperfection, including uncertainty and imprecision. An extension of stochastic programming with recourse is used to tackle the problem. This approach aims to regain the feasibility of the routes that missed one or more of the customer time windows due to the uncertain nature of the problem. A memetic algorithm is devised to solve the problem on an adaptation of literature instances.

The class imbalance issue involves many real-world domains such as fraud detection, medical diagnosis, intrusion detection, etc. Most classification algorithms tend to perform poorly when the training dataset is class-imbalanced. This problem gets more challenging in the presence of other factors such as class-overlapping and noise. Among many methods, undersampling is a simple and efficient approach which re-balances the imbalanced dataset by removing majority samples. In this paper, we propose a novel method named Evidential Undersampling (EVUS), which is a re-sampling approach based on the theory of evidence. To avoid removing meaningful samples, each majority object is assigned a soft evidential label to gain more information about its location, then majority samples which are considered ambiguous or noisy by our framework, are eliminated from the training set. The conducted results with CART and SVM show that our proposal outperformed other well-known undersampling methods according to the AUC metric.