We address the pattern explosion problem in pattern mining by proposing an interactive learning framework that combines nonlinear utility aggregation with geometry-aware query selection. Our method models user preferences through a Choquet integral over multiple interestingness measures and exploits the geometric structure of the version space to guide the selection of informative comparisons. A branch-and-bound strategy with tight distance bounds enables efficient identification of queries near the decision boundary. Experiments on UCI datasets show that our approach outperforms existing methods such as ChoquetRank, achieving better ranking accuracy with fewer user interactions.

Event Causality Identification (ECI) aims to detect causal relationships between events in textual contexts. Existing ECI models predominantly rely on supervised methodologies, suffering from dependence on large-scale annotated data. Although Large Language Models (LLMs) enable zero-shot ECI, they are prone to causal hallucination-erroneously establishing spurious causal links. To address these challenges, we propose MEFA, a novel zero-shot framework based on Multi-source Evidence Fuzzy Aggregation. First, we decompose causality reasoning into three main tasks (temporality determination, necessity analysis, and sufficiency verification) complemented by three auxiliary tasks. Second, leveraging meticulously designed prompts, we guide LLMs to generate uncertain responses and deterministic outputs. Finally, we quantify LLM's responses of sub-tasks and employ fuzzy aggregation to integrate these evidence for causality scoring and causality determination. Extensive experiments on three benchmarks demonstrate that MEFA outperforms second-best unsupervised baselines by 6.2% in F1-score and 9.3% in precision, while significantly reducing hallucination-induced errors. In-depth analysis verify the effectiveness of task decomposition and the superiority of fuzzy aggregation.

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty (EU) -- due to incomplete knowledge -- requires richer representations than those offered by classical probability. Imprecise probability (IP) theory offers such models, capturing ambiguity and partial belief. This has driven growing interest in imprecise probabilistic machine learning (IPML), where inference and decision-making rely on broader uncertainty models -- highlighting the need for metrics beyond classical probability. This work introduces the Integral Imprecise Probability Metric (IIPM) framework, a Choquet integral-based generalisation of classical Integral Probability Metric (IPM) to the setting of capacities -- a broad class of IP models encompassing many existing ones, including lower probabilities, probability intervals, belief functions, and more. Theoretically, we establish conditions under which IIPM serves as a valid metric and metrises a form of weak convergence of capacities. Practically, IIPM not only enables comparison across different IP models but also supports the quantification of epistemic uncertainty within a single IP model. In particular, by comparing an IP model with its conjugate, IIPM gives rise to a new class of EU measures -- Maximum Mean Imprecision -- which satisfy key axiomatic properties proposed in the Uncertainty Quantification literature. We validate MMI through selective classification experiments, demonstrating strong empirical performance against established EU measures, and outperforming them when classical methods struggle to scale to a large number of classes. Our work advances both theory and practice in IPML, offering a principled framework for comparing and quantifying epistemic uncertainty under imprecision.

This paper introduces feature subset weighting using monotone measures for distance-based supervised learning. The Choquet integral is used to define a distance metric that incorporates these weights. This integration enables the proposed distances to effectively capture non-linear relationships and account for interactions both between conditional and decision attributes and among conditional attributes themselves, resulting in a more flexible distance measure. In particular, we show how this approach ensures that the distances remain unaffected by the addition of duplicate and strongly correlated features. Another key point of this approach is that it makes feature subset weighting computationally feasible, since only $m$ feature subset weights should be calculated each time instead of calculating all feature subset weights ($2^m$), where $m$ is the number of attributes. Next, we also examine how the use of the Choquet integral for measuring similarity leads to a non-equivalent definition of distance. The relationship between distance and similarity is further explored through dual measures. Additionally, symmetric Choquet distances and similarities are proposed, preserving the classical symmetry between similarity and distance. Finally, we introduce a concrete feature subset weighting distance, evaluate its performance in a $k$-nearest neighbors (KNN) classification setting, and compare it against Mahalanobis distances and weighted distance methods.

The COVID-19 pandemic has profoundly impacted billions globally. It challenges public health and healthcare systems due to its rapid spread and severe respiratory effects. An effective strategy to mitigate the COVID-19 pandemic involves integrating testing to identify infected individuals. While RT-PCR is considered the gold standard for diagnosing COVID-19, it has some limitations such as the risk of false negatives. To address this problem, this paper introduces a novel Deep Learning Diagnosis System that integrates pre-trained Deep Convolutional Neural Networks (DCNNs) within an ensemble learning framework to achieve precise identification of COVID-19 cases from Chest X-ray (CXR) images. We combine feature vectors from the final hidden layers of pre-trained DCNNs using the Choquet integral to capture interactions between different DCNNs that a linear approach cannot. We employed Sugeno-$\lambda$ measure theory to derive fuzzy measures for subsets of networks to enable aggregation. We utilized Differential Evolution to estimate fuzzy densities. We developed a TensorFlow-based layer for Choquet operation to facilitate efficient aggregation, due to the intricacies involved in aggregating feature vectors. Experimental results on the COVIDx dataset show that our ensemble model achieved 98\% accuracy in three-class classification and 99.50\% in binary classification, outperforming its components-DenseNet-201 (97\% for three-class, 98.75\% for binary), Inception-v3 (96.25\% for three-class, 98.50\% for binary), and Xception (94.50\% for three-class, 98\% for binary)-and surpassing many previous methods.

Sensor fusion combines data from multiple sensor sources to improve reliability, robustness, and accuracy of data interpretation. The Fuzzy Integral (FI), in particular, the Choquet integral (ChI), is often used as a powerful nonlinear aggregator for fusion across multiple sensors. However, existing supervised ChI learning algorithms typically require precise training labels for each input data point, which can be difficult or impossible to obtain. Additionally, prior work on ChI fusion is often based only on the normalized fuzzy measures, which bounds the fuzzy measure values between [0, 1]. This can be limiting in cases where the underlying scales of input data sources are bipolar (i.e., between [-1, 1]). To address these challenges, this paper proposes a novel Choquet integral-based fusion framework, named Bi-MIChI (pronounced "bi-mi-kee"), which uses bi-capacities to represent the interactions between pairs of subsets of the input sensor sources on a bi-polar scale. This allows for extended non-linear interactions between the sensor sources and can lead to interesting fusion results. Bi-MIChI also addresses label uncertainty through Multiple Instance Learning, where training labels are applied to "bags" (sets) of data instead of per-instance. Our proposed Bi-MIChI framework shows effective classification and detection performance on both synthetic and real-world experiments for sensor fusion with label uncertainty. We also provide detailed analyses on the behavior of the fuzzy measures to demonstrate our fusion process.

This paper introduces a novel Choquet distance using fuzzy rough set based measures. The proposed distance measure combines the attribute information received from fuzzy rough set theory with the flexibility of the Choquet integral. This approach is designed to adeptly capture non-linear relationships within the data, acknowledging the interplay of the conditional attributes towards the decision attribute and resulting in a more flexible and accurate distance. We explore its application in the context of machine learning, with a specific emphasis on distance-based classification approaches (e.g. k-nearest neighbours). The paper examines two fuzzy rough set based measures that are based on the positive region. Moreover, we explore two procedures for monotonizing the measures derived from fuzzy rough set theory, making them suitable for use with the Choquet integral, and investigate their differences.

In this paper, we propose an interactive genetic algorithm for solving multi-objective combinatorial optimization problems under preference imprecision. More precisely, we consider problems where the decision maker's preferences over solutions can be represented by a parameterized aggregation function (e.g., a weighted sum, an OWA operator, a Choquet integral), and we assume that the parameters are initially not known by the recommendation system. In order to quickly make a good recommendation, we combine elicitation and search in the following way: 1) we use regret-based elicitation techniques to reduce the parameter space in a efficient way, 2) genetic operators are applied on parameter instances (instead of solutions) to better explore the parameter space, and 3) we generate promising solutions (population) using existing solving methods designed for the problem with known preferences. Our algorithm, called RIGA, can be applied to any multi-objective combinatorial optimization problem provided that the aggregation function is linear in its parameters and that a (near-)optimal solution can be efficiently determined for the problem with known preferences. We also study its theoretical performances: RIGA can be implemented in such way that it runs in polynomial time while asking no more than a polynomial number of queries. The method is tested on the multi-objective knapsack and traveling salesman problems. For several performance indicators (computation times, gap to optimality and number of queries), RIGA obtains better results than state-of-the-art algorithms.

In this preference elicitation setting, our focus is on determining the parameters of a decision model that accurately captures the pairwise preferences of a Decision Maker (DM) over subsets, by comparing subsets of elements. The preferences are depicted using a highly adaptable model whose versatility stems from its ability to incorporate positive or negative synergies between elements [24]. Moreover, we provide an ordinally robust approach, in the sense that the preferences we infer do not rely on arbitrarily specified parameter values, but on the set of all parameter values that are compatible with the observed preferences. Importantly, another distinctive feature of our approach is its ability to learn the parameter set itself (not only the values of parameters). The preference model we consider can be used in different contexts, depending on the nature of the subsets we are comparing. The subsets are represented by binary vectors, showing the presence or absence of an element in the subset. The elements of a subset can be for example: individuals (in the comparison of coalitions, teams, etc.), binary attributes (in the comparison of multiattribute alternatives), objects (in the comparison of subsets in a subset choice problem), etc. For illustration, a toy example of such an elicitation context could be a coffee shop trying to determine its customers' favorite frozen yogurt flavor combination by offering them to test a small number of flavor combinations rather than having them taste each combination.

Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision making, image processing, machine learning for both classification, and regression. Tools for measure identification have been built. In short, as non-additive measures are more general than additive ones (i.e., than probabilities), they have better modeling capabilities allowing to model situations and problems that cannot be modeled by the latter. See e.g. the application of non-additive measures and the Choquet integral to model both Ellsberg paradox and Allais paradox. Because of that, there is an increasing need to analyze non-additive measures. The need for distances and similarities to compare them is no exception. Some work has been done for defining $f$-divergence for them. In this work we tackle the problem of defining the optimal transport problem for non-additive measures. Distances for pairs of probability distributions based on the optimal transport are extremely used in practical applications, and they are being studied extensively for their mathematical properties. We consider that it is necessary to provide appropriate definitions with a similar flavour, and that generalize the standard ones, for non-additive measures. We provide definitions based on the M\"obius transform, but also based on the $(\max, +)$-transform that we consider that has some advantages. We will discuss in this paper the problems that arise to define the transport problem for non-additive measures, and discuss ways to solve them. In this paper we provide the definitions of the optimal transport problem, and prove some properties.