查看更多>>摘要：In multi-label learning, feature selection is a crucial step for enhancing model performance and reducing computational complexity. However, due to the interdependence among labels and the high dimensionality of feature sets, traditional single-label feature selection methods often underperform in multi-label scenarios. Moreover, many existing feature selection methods typically require a comprehensive evaluation of all features and samples in each iteration, resulting in high computational complexity. To address this issue, this paper proposes a feature selection algorithm based on fuzzy conditional entropy within the framework of fuzzy rough set theory. The method gradually identifies optimal features through iterative optimization and systematically filters out features and samples that do not contribute to the current feature subset. Specifically, the filtered features and samples are incorporated into redundant feature and sample sets, thereby dynamically excluding these redundant elements in subsequent iterations and avoiding unnecessary computations. Experiments conducted on 10 multi-label datasets demonstrate that the proposed algorithm outperforms eight other methods in terms of performance.
查看更多>>摘要：We consider the problem of aggregating belief models elicited by experts when these are expressed by means of coherent lower previsions. These constitute a framework general enough so as to include as particular cases not only probability measures but also the majority of models from imprecise probability theory. Although the aggregation problem has already been tackled in the literature, our contribution provides a unified view by gathering a number of rationality criteria and aggregation rules studied in different papers. Specifically, we consider six aggregation rules and twenty rationality criteria. We exhaustively analyse the relationships between the rules, the properties satisfied by each rule and the characterisations of the rules in terms of the criteria.
查看更多>>摘要：Outlier detection is an important part of the process of carrying out data mining and analysis and has been applied to many fields. Existing methods are typically anchored in a single-sample processing paradigm, where the processing unit is each individual and single-granularity sample. This processing paradigm is inefficient and ignores the multi-granularity features inherent in data. In addition, these methods often overlook the uncertainty information present in the data. To remedy the above-mentioned shortcomings, we propose an unsupervised outlier detection method based on Granular-Ball Fuzzy Granules (GBFG). GBFG adopts a granular-ball-based computing paradigm, where the fundamental processing units are granular-balls. This shift from individual samples to granular-balls enables GBFG to capture the overall data structure from a multi-granularity perspective and improve the performance of outlier detection. Subsequently, we calculate the outlier factor based on the outlier degrees of the granular-ball fuzzy granules to which the sample belongs, serving as a measure of the outlier degrees of samples. The experimental results prove that GBFG has a remarkable performance compared with the existing excellent algorithms. The code of GBFG is publicly available on https://github.com/Mxeron/GBFG.
查看更多>>摘要：Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied modelling, it is critical to assess how robust the inferences on certain target variables are to changes in the model. In Bayesian networks, these analyses fall under the umbrella of sensitivity analysis, which is most commonly carried out by quantifying dissimilarities using Kullback-Leibler information measures. We argue that robustness methods based instead on the total variation distance provide simple and more valuable bounds on robustness to misspecification, which are both formally justifiable and transparent. We introduce a novel measure of dependence in conditional probability tables called the diameter to derive such bounds. This measure quantifies the strength of dependence between a variable and its parents. Furthermore, the diameter is a versatile measure that can be applied to a wide range of sensitivity analysis tasks. It is particularly useful for quantifying edge strength, assessing influence between pairs of variables, detecting asymmetric dependence, and amalgamating levels of variables. This flexibility makes the diameter an invaluable tool for enhancing the robustness and interpretability of Bayesian network models in applied risk management and decision support.
查看更多>>摘要：For several types of information relations, the induced rough sets system RS does not form a lattice but only a partially ordered set. However, by studying its Dedekind-MacNeille completion DM(RS), one may reveal new important properties of rough set structures. Building upon D. Umadevi's work on describing joins and meets in DM(RS), we previously investigated pseudo-Kleene algebras defined on DM(RS) for reflexive relations. This paper delves deeper into the order-theoretic properties of DM(RS) in the context of reflexive relations. We describe the completely join-irreducible elements of DM(RS) and characterize when DM(RS) is a spatial completely distributive lattice. We show that even in the case of a non-transitive reflexive relation, DM(RS) can form a Nelson algebra, a property generally associated with quasiorders. We introduce a novel concept, the core of a relational neighbourhood, and use it to provide a necessary and sufficient condition for DM(RS) to determine a Nelson algebra.
查看更多>>摘要：We investigate the computational problem of determining the set of acceptable arguments in abstract argumentation wrt. credulous and skeptical reasoning under grounded, complete, stable, and preferred semantics. In particular, we investigate the computational complexity of that problem and its verification variant, and develop several algorithms for all problem variants, including two baseline approaches based on iterative acceptability queries and extension enumeration, and some optimised versions. We experimentally compare the runtime performance of these algorithms: our results show that our newly optimised algorithms significantly outperform the baseline algorithms in most cases.
查看更多>>摘要：Conflict is ubiquitous in life. Conflict analysis is a tool for understanding conflicts, whose aim is to analyze the conflict situations in data to help decision makers avoid risks. Existing conflict analysis methods mainly focus on single-source data. However, the emergence of big data era has generated more complex data, such as multi-source data obtained from different perspectives, which can capture details that single-source data is missing. Not only that, most data also exhibit characteristics of fuzziness. The above situations make it more challenging to construct a conflict analysis model in the environment of multi-source fuzzy data to acquire a compliant decision. Therefore, conflict analysis for multi-source fuzzy data is a worthy research topic. However, the existing few studies on multi-source fuzzy data either favor attribute values or ignore conflict resolution, which reduces the conflict resolution performance due to underutilizing attribute information. To solve the above problem, we divide the attribute values of multi-source fuzzy data into three attitude intervals to distinguish different attitudes of agents. Then, we propose a function to measure conflict and construct a conflict analysis model for a multi-source fuzzy formal context. Additionally, we put forward an information fusion method based on the minimum of fuzzy entropy, whose purpose is to achieve conflict resolution quickly. Finally, experiments conducted on 18 datasets demonstrate that our information fusion method can achieve conflict resolution effectively, and provide a useful reference for decision-makers.
查看更多>>摘要：The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian graphical models can be blurred by additional correlation between the observed variables that is incurred by the latent variables. A standard approach for this problem is a latent version of the graphical lasso that splits the inverse covariance matrix into a sparse and a low-rank part that are penalized separately. This approach has recently been extended successfully to H & uuml;sler-Reiss graphical models, which can be considered as an analogue of Gaussian graphical models in extreme value statistics. In this paper we propose a generalization of structure learning for Gaussian and H & uuml;sler-Reiss graphical models via the flexible Golazo penalty. This allows us to introduce latent versions of for example the adaptive lasso, positive dependence constraints or predetermined sparsity patterns, and combinations of those. We develop algorithms for both latent graphical models with the Golazo penalty and demonstrate it on simulated and real data.
查看更多>>摘要：This paper examines the approximation capabilities of lattice integral transforms and their compositions in reconstructing lattice-valued functions. By introducing an integral kernel Q on the function domain, we define the concept of a Q-inverse integral kernel, which generalizes the traditional inverse kernel defined as a transposed integral kernel. Leveraging these Q-inverses, we establish upper and lower bounds for a transformed version of the original function induced by the integral kernel Q. The quality of approximation is analyzed using a lattice-based modulus of continuity, specifically designed for functions valued in complete residuated lattices. Additionally, under specific conditions, we demonstrate that the approximation quality for extensional functions with respect to the kernel Q can be estimated through the integral of the square of Q, and in certain cases, these extensional functions can be perfectly reconstructed. The theoretical findings, illustrated through examples, provide a strong foundation for further theoretical advancement and practical applications.
NETL
NSTL
Elsevier