International Journal of Approximate Reasoning最新文献_第2页

Fuzzy neighborhood components analysis: Supervised dimensionality reduction under uncertain labels 模糊邻域成分分析：不确定标签下的监督降维

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-04-01 Epub Date: 2026-01-24 DOI: 10.1016/j.ijar.2026.109635

Mohd Aquib , Mohd Suhail Naim

Real-world supervision is often soft or uncertain due to annotator disagreement, class ambiguity, and distribution shift, yet most dimensionality-reduction methods and classical Neighborhood Components Analysis (NCA) in particular, assume hard labels. We propose Fuzzy Neighborhood Components Analysis (Fuzzy-NCA), a linear metric-learning method that directly optimizes a stochastic k-Nearest Neighbors (kNN) objective under fuzzy supervision. Each sample carries a row-stochastic membership vector over classes; pairwise supervision is defined by a principled fuzzy overlap between membership vectors, optionally sharpened by a power parameter to emphasize confident assignments. Ambiguous anchors can be attenuated via an entropy-based reliability weight, yielding an objective that maximizes a reliability-weighted expected fuzzy hit rate. The formulation reduces exactly to classical NCA when memberships are one-hot and admits a closed-form gradient, enabling efficient optimization with standard first-order methods. To scale training, we restrict stochastic neighbors to an input-space k-nearest-neighbor graph, which preserves local geometry while reducing the per-iteration complexity from quadratic to near-linear in the dataset size. The framework is compatible with multiple ways of constructing fuzzy supervision including label smoothing, fuzzy kNN, calibrated posteriors, and type-2 fuzzy reductions making it broadly applicable. Empirically, across a diverse suite of benchmarks, Fuzzy-NCA yields stable, discriminative embeddings under noisy or ambiguous labels, improving both linear separability and neighborhood quality and exhibiting consistent robustness across settings.

现实世界的监督通常是软的或不确定的，因为注释者的分歧，类的模糊性和分布的转移，然而大多数降维方法和经典的邻域成分分析（NCA），特别是，假设硬标签。我们提出了模糊邻域成分分析（Fuzzy- nca），这是一种线性度量学习方法，在模糊监督下直接优化随机k近邻（kNN）目标。每个样本在类上携带一个行随机隶属向量；两两监督由隶属向量之间的原则模糊重叠定义，可选地通过功率参数锐化以强调自信分配。模糊锚可以通过基于熵的可靠性权重来减弱，从而产生一个最大化可靠性加权期望模糊命中率的目标。当成员是一个热点时，该公式精确地减少到经典的NCA，并承认一个封闭形式的梯度，使有效的优化与标准的一阶方法。为了扩展训练，我们将随机邻居限制为输入空间的k近邻图，这保留了局部几何形状，同时将数据集大小的每次迭代复杂度从二次型降低到近线性。该框架兼容多种构建模糊监督的方法，包括标签平滑、模糊kNN、校准后验和2型模糊约简，使其具有广泛的适用性。从经验上看，在不同的基准测试中，Fuzzy-NCA在噪声或模糊标签下产生稳定的判别嵌入，提高了线性可分性和邻域质量，并在不同设置中表现出一致的鲁棒性。

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引用次数: 0

On the edges of characteristic imset polytopes 在特征压印多面体的边缘上

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-04-01 Epub Date: 2025-12-06 DOI: 10.1016/j.ijar.2025.109606

Svante Linusson, Petter Restadh, Liam Solus

The basic problem of causal discovery is concerned with estimating a directed acyclic graph (DAG) representing the dependence relations in multivariate data. Several successful causal discovery algorithms have optimization-based aspects, which operate via a set of rules for searching the space of DAGs. Recent results have revealed that the edge graph of the so-called characteristic imset polytope,

{C I M}_{p}

, can provide a diverse set of such rules. Characterizing the edge graph of

{C I M}_{p}

is a generally challenging problem. However, many algorithms first estimate the adjacencies in the causal DAG, in the form of an undirected graph G, prior to orienting the edges. In this regime, knowledge of the subpolytope

{C I M}_{G}

defined for DAGs with adjacencies specified by G is valuable. In this paper, we characterize the edge graph of

{C I M}_{G}

when G is an undirected tree, providing the first family of characteristic imset polytopes for which the edge graph is completely understood. These results are applied to give a new causal discovery algorithm that estimates a polytree representing the dependencies in the given multivariate data. Our algorithm is shown to out-perform comparable methods on both real and synthetic data. Our results also reveal connections between characteristic imset polytopes and the well-studied stable set polytopes from combinatorial optimization.

因果发现的基本问题是如何估计多变量数据中表示依赖关系的有向无环图。一些成功的因果发现算法具有基于优化的方面，通过一组规则来搜索dag空间。最近的研究结果表明，所谓的特征嵌套多面体（CIMp）的边图可以提供一组不同的规则。描述CIMp的边图是一个普遍具有挑战性的问题。然而，许多算法首先以无向图G的形式估计因果DAG中的邻接关系，然后再定向边缘。在这种情况下，为具有G指定邻接的dag定义的亚多体CIMG的知识是有价值的。在本文中，我们刻画了当G是无向树时CIMG的边图，给出了其边图完全可理解的第一族特征嵌套多面体。这些结果应用于给出一种新的因果发现算法，该算法估计表示给定多变量数据中的依赖关系的多树。我们的算法在真实数据和合成数据上都优于可比的方法。我们的研究结果还揭示了特征嵌套多面体与从组合优化中得到的稳定集多面体之间的联系。

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引用次数: 0

Generalized fiducial inference on differentiable manifolds 关于可微流形的广义基准推理

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-12-20 DOI: 10.1016/j.ijar.2025.109618

A.C. Murph , J.P. Williams , J. Hannig

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer graphics, and geology. This new approach uses generalized fiducial inference (GFI) to obtain a posterior-like distribution on the manifold, without needing to know local parameterizations that map to the constrained space from an unconstrained Euclidean space. Using mathematical tools from Riemannian geometry, we construct a constrained generalized fiducial distribution (CGFD). A Bernstein-von Mises-type result for the CGFD, which provides intuition for how the desirable asymptotic qualities of the unconstrained generalized fiducial distribution are inherited by the CGFD, is provided. To illustrate the practical use of the CGFD, we provide a proof-of-concept example in the context of a linear logspline density estimation problem, and demonstrate that CGFD-based confidence sets exhibit desirable coverage properties via simulation. As an application, we fit a CGFD to COVID-19 case count data from North Carolina, USA.

我们提出了一种新的方法来对嵌入欧几里得空间的黎曼流形中取值的参数进行推理。这种形式的参数空间在很多领域都很普遍，包括化学、物理、计算机图形学和地质学。这种新方法使用广义基准推理（GFI）来获得流形上的后验分布，而不需要知道从无约束欧几里德空间映射到约束空间的局部参数化。利用黎曼几何中的数学工具，构造了一个约束广义基准分布（CGFD）。给出了CGFD的一个Bernstein-von mises型结果，直观地说明了CGFD如何继承无约束广义基准分布的理想渐近性质。为了说明CGFD的实际应用，我们在线性对数样条密度估计问题的背景下提供了一个概念验证示例，并通过模拟证明基于CGFD的置信集具有理想的覆盖特性。作为一项应用，我们将CGFD与美国北卡罗来纳州的COVID-19病例数数据相匹配。

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引用次数: 0

Sweep transform on imaginary matrices and its application to parameter estimation with Gaussian belief functions 虚矩阵的扫描变换及其在高斯信念函数参数估计中的应用

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-11-29 DOI: 10.1016/j.ijar.2025.109607

Liping Liu

Gaussian belief functions admit matrix representations, with their combination reduced to matrix summation under Dempster’ s rule. However, the incorporation of deterministic and logic knowledge under ignorance introduces division-by-zero issues, often requiring symbolic calculus—a method that becomes intractable for large matrices. This paper proposes the sweep transform on imaginary matricesas a solution to this challenge and demonstrates its utility for parameter estimation by combining data represented as Gaussian belief functions. It advances the theory of sweep transforms by showing that, when extended to imaginary numbers, a sweep transform with a symmetric matrix as the pivot can be decomposed into a sequence of sweeps using the matrix’ s leading diagonal elements as pivots. Notably, such reducibility does not hold when restricted to real numbers. The result gives rises to a novel approach to inverting structured symmetric matrices, which may not be positive definite, without requiring permutations even in the presence of zero pivots.

高斯信念函数允许矩阵表示，它们的组合在Dempster规则下简化为矩阵和。然而，在无知的情况下，确定性和逻辑知识的结合引入了除以零的问题，通常需要符号演算——一种对于大型矩阵变得难以处理的方法。本文提出了对虚矩阵的扫描变换作为解决这一挑战的方法，并通过将表示为高斯信念函数的数据组合在一起，证明了它在参数估计中的实用性。通过证明当扩展到虚数时，以对称矩阵为枢轴的扫描变换可以分解为以矩阵的前导对角元素为枢轴的扫描序列，提出了扫描变换的理论。值得注意的是，这种可约性在实数上并不成立。结果提出了一种新的方法来反演结构对称矩阵，它可能不是正定的，即使在零轴存在的情况下也不需要置换。

引用次数: 0

An axiomatic development of Pereira-Stern e-value as a measure of support for statistical hypotheses Pereira-Stern e值作为统计假设支持度度量的公理发展

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-12-25 DOI: 10.1016/j.ijar.2025.109622

Yasmin F. Cavaliere, Luís G. Esteves, Victor Fossaluza

Testing hypotheses is fundamental to any scientific investigation or data-driven decision-making process. Since Neyman and Pearson systematized hypothesis testing, this statistical procedure has significantly contributed to the development of competing theories of statistical inference. Common approaches to hypothesis testing include significance tests, most powerful tests, likelihood ratio tests, and Bayesian tests. However, practitioners often use evidence measures, such as p-values, the Pereira-Stern e-value and likelihood ratio statistics, in lieu of the reject-or-fail-to-reject approach proposed by Neyman and Pearson, as they provide a more nuanced understanding of statistical hypotheses from data. This study proposes an axiomatic development of belief relations representing the extent to which sample data support a statistical hypothesis, which is consistent with a few logical requirements that capture, in a sense, the Onus Probandi principle in law. It also examines whether the above-mentioned evidence measures are reasonable mathematical representations of such belief relations, that is, of how much a sample supports a hypothesis. It shows that for discrete parameter and sample spaces, the measure of evidence by Pereira and Stern is a fair representation of such a belief relation, especially for Bayesian decision-makers as it formally considers the uncertainty one has about the unknown parameter at the same time it induces a relation that coincides with the belief relation meeting the axioms. This result renders the Pereira-Stern e-value a genuine measure of support for statistical hypotheses in the discrete case, in addition to its recognized importance in the continuous case.

检验假设是任何科学调查或数据驱动决策过程的基础。自从Neyman和Pearson将假设检验系统化以来，这一统计过程对统计推断的竞争理论的发展做出了重大贡献。假设检验的常用方法包括显著性检验、最有力检验、似然比检验和贝叶斯检验。然而，从业者经常使用证据度量，如p值，Pereira-Stern e值和似然比统计，而不是Neyman和Pearson提出的拒绝或不拒绝方法，因为它们从数据中提供了对统计假设的更细致的理解。本研究提出了一个信念关系的公理发展，代表了样本数据支持统计假设的程度，这与一些逻辑要求是一致的，在某种意义上，法律上的举证责任原则。它还检验了上述证据度量是否是这种信念关系的合理数学表示，即样本支持假设的程度。结果表明，对于离散参数和样本空间，Pereira和Stern的证据度量是这种信念关系的公平表示，特别是对于贝叶斯决策者，因为它在形式上考虑了一个人对未知参数的不确定性的同时，它推导出与满足公理的信念关系一致的关系。这一结果使得佩雷拉-斯特恩e值除了在连续情况下的公认重要性之外，在离散情况下是支持统计假设的真正度量。

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引用次数: 0

Game-theoretic multi-granularity consensus adjustment for social network group decision-making 社会网络群体决策的博弈论多粒度共识调整

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-12-08 DOI: 10.1016/j.ijar.2025.109610

Hanzhong Hou , Chao Zhang , Deyu Li , Wentao Li

The continuous trend development of information intelligence has made social network group decision-making (SN-GDM) increasingly important. However, in the context of SN-GDM, there are three key challenges: how to properly handle the decline in the trust propagation efficiency; the single granularity consensus adjustment strategy may not fully consider the impact of groups with high consensus on costs and the different cooperation intention of subgroups; traditional methods often face challenges in determining high-performance classification thresholds. In response to the above issues, the solution involves reconstructing trust relationships and optimizing clustering via the Leiden algorithm (LA) and structural holes (SHs). Moreover, multi-granularity consensus adjustment is implemented using game theory while classification thresholds are refined with game-theoretic rough sets (GTRSs). More specifically, firstly, the discount rate of trust propagation intermediaries and path reliability are considered to conduct indirect trust propagation and multipath fusion, and the cooperation index (CI) is obtained based on trust relationships and similarities. Secondly, LA is used to cluster DMs, with the CI as the edge weight, to ensure that the community reflects social relationships and opinion consensus. The weight of decision-makers (DMs) and subgroups are objectively determined by comprehensively integrating SHs, CI, similarity and in-degree centrality. Thirdly, a multi-granularity consensus adjustment method involving game theory is proposed. This method considers three adjustment scenarios: joint adjustment, cooperative game, and non-cooperative game, to obtain the optimal adjustment strategy while ensuring the individual benefit of participants. Then, the generality and accuracy of classification thresholds are improved via the application of GTRSs. Finally, a case study is conducted on the evaluation of scenic spots via a questionnaire survey, verifying the feasibility and effectiveness of the proposed method.

随着信息智能化趋势的不断发展，社会网络群体决策（social network group decision, SN-GDM）变得越来越重要。然而，在SN-GDM的背景下，有三个关键的挑战：如何妥善处理信任传播效率的下降；单粒度共识调整策略可能没有充分考虑高共识群体对成本的影响以及子群体不同的合作意向；传统方法在确定高性能分类阈值方面经常面临挑战。针对上述问题，通过Leiden算法（LA）和结构洞（SHs）进行信任关系重构和聚类优化。利用博弈论实现多粒度共识调整，利用博弈论粗糙集（GTRSs）细化分类阈值。具体而言，首先考虑信任传播中介的贴现率和路径可靠性，进行间接信任传播和多路径融合，并基于信任关系和相似度得到合作指数（CI）；其次，采用LA对dm进行聚类，以CI作为边缘权重，确保社区反映社会关系和意见共识；通过综合综合SHs、CI、相似度和度中心性，客观确定决策者和子群体的权重。第三，提出了一种涉及博弈论的多粒度共识调整方法。该方法考虑联合调整、合作博弈和非合作博弈三种调整情景，在保证参与者个体利益的前提下，获得最优的调整策略。然后，通过gtrs的应用，提高分类阈值的通用性和准确性。最后，通过问卷调查对景区进行评价，验证了所提方法的可行性和有效性。

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引用次数: 0

Measuring external conflict in Dempster-Shafer theory based on Kantorovich problems 基于Kantorovich问题的Dempster-Shafer理论中的外部冲突度量

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-11-09 DOI: 10.1016/j.ijar.2025.109597

Andrey G. Bronevich , Alexander E. Lepskiy

In the paper, we consider three possible types of external conflict in Dempster-Shafer theory and propose its measurement based on functionals evaluating intersection, inclusion and distance between random sets. All proposed functionals can be viewed as extensions of known functionals like Jaccard metric, Jaccard index, and Dice coefficient from usual sets to random sets based on the solutions of the Kantorovich problems.

在本文中，我们考虑了Dempster-Shafer理论中三种可能的外部冲突类型，并提出了基于评估随机集之间的交集、包含和距离的泛函度量方法。所有提出的泛函都可以看作是已知泛函的扩展，如Jaccard度量、Jaccard指数和Dice系数，从通常集合到基于Kantorovich问题解的随机集合。

引用次数: 0

Towards a Δ-based metric framework for NMΔ: Δ truth degree and Δ logic metric space 对NMΔ： Δ真度和Δ逻辑度量空间的Δ-based度量框架

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-12-18 DOI: 10.1016/j.ijar.2025.109619

Bo Wang , Xiaoquan Xu

The Nilpotent Minimum logic expanded with the Baaz-Monteiro Δ connective (NM_Δ) offers a rich framework for reasoning with vagueness, yet a systematic quantitative and topological analysis of it remains largely unexplored. To bridge this gap, this paper develops a novel theoretical framework based on the formula-induced function method. We first define the Δ truth degree of a formula in NM_Δ, investigating its fundamental properties and proving its soundness under key inference rules such as MP, HS, as well as union and intersection inferences. We further derive a computational expression for the truth degree of generalized conjunctive formulae. Secondly, building on this, we introduce the concepts of Δ similarity degree and Δ pseudo-distance, establishing their essential properties. Finally. this construction yields the Δ logic metric space

(F (S), ρ_{n}^{Δ})

. Within this space, we perform a preliminary topological analysis, proving the continuity of the fundamental logical operators (Δ,  ∼ ,  → , ∧, ∨) with respect to the Δ pseudo-distance

ρ_{n}^{Δ}

and proving that this space contains no isolated points. The significance of this work lies in providing the necessary foundational framework and tools for future exploration of convergence, density, and other topological properties in non-classical logic systems.

用Baaz-Monteiro Δ连接（NMΔ）展开的幂零最小逻辑为模糊推理提供了丰富的框架，但对它的系统定量和拓扑分析在很大程度上仍未被探索。为了弥补这一缺陷，本文基于公式诱导函数法提出了一种新的理论框架。我们首先在NMΔ中定义了一个公式的Δ真度，研究了它的基本性质，并证明了它在关键推理规则（如MP、HS以及并和交推理）下的正确性。进一步导出了广义合式真度的计算表达式。其次，在此基础上引入Δ相似度和Δ伪距离的概念，建立了它们的基本性质。最后。这种构造产生Δ逻辑度量空间（F(S),ρnΔ）。在这个空间内，我们进行了初步的拓扑分析，证明了基本逻辑算子（Δ， ~ ， → ，∧,∨）关于Δ伪距离ρnΔ的连续性，并且证明了这个空间不包含孤立点。这项工作的意义在于为未来探索非经典逻辑系统的收敛性、密度和其他拓扑性质提供必要的基础框架和工具。

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引用次数: 0

Neural approaches to SAT solving: Design choices and interpretability 解决SAT的神经方法：设计选择和可解释性

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-12-05 DOI: 10.1016/j.ijar.2025.109609

David Mojžíšek , Jan Hůla , Ziwei Li , Ziyu Zhou , Mikoláš Janota

In this contribution, we provide a comprehensive evaluation of graph neural networks applied to Boolean satisfiability problems, accompanied by an intuitive explanation of the mechanisms enabling the model to generalize to different instances. We introduce several training improvements, particularly a novel closest assignment supervision method that dynamically adapts to the model’s current state, significantly enhancing performance on problems with larger solution spaces. Our experiments demonstrate the suitability of variable-clause graph representations with recurrent neural network updates, which achieve good accuracy on SAT assignment prediction while reducing computational demands. We extend the base graph neural network into a diffusion model that facilitates incremental sampling and can be effectively combined with classical techniques like unit propagation. Through analysis of embedding space patterns and optimization trajectories, we show how these networks implicitly perform a process very similar to continuous relaxations of MaxSAT, offering an interpretable view of their reasoning process. This understanding guides our design choices and explains the ability of recurrent architectures to scale effectively at inference time beyond their training distribution, which we demonstrate with test-time scaling experiments.

在这篇文章中，我们提供了应用于布尔可满足性问题的图神经网络的综合评估，并伴随着对使模型能够推广到不同实例的机制的直观解释。我们引入了一些训练改进，特别是一种新的最接近分配监督方法，它可以动态地适应模型的当前状态，显著提高了在具有较大解空间的问题上的性能。我们的实验证明了变量子句图表示与递归神经网络更新的适用性，在减少计算需求的同时，在SAT分配预测上取得了良好的准确性。我们将基图神经网络扩展为一个扩散模型，该模型便于增量采样，并且可以有效地与单元传播等经典技术相结合。通过对嵌入空间模式和优化轨迹的分析，我们展示了这些网络如何隐式地执行与MaxSAT连续松弛非常相似的过程，并提供了其推理过程的可解释视图。这种理解指导了我们的设计选择，并解释了循环架构在超出其训练分布的推理时间有效扩展的能力，我们通过测试时间扩展实验证明了这一点。

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引用次数: 0

Fuzzy rules with quantifiers as weights 以量词作为权重的模糊规则

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2026-03-01 Epub Date: 2025-11-28 DOI: 10.1016/j.ijar.2025.109600

Martina Daňková , Dana Hliněná

In this paper, we explore the use of General Unary Hypotheses Automaton quantifiers and provide representations for their specific subclasses. Furthermore, we focus explicitly on implicational quantifiers for analyzing specific relational dependencies. We discuss their suitability in fuzzy modeling and demonstrate their integration with appropriate fuzzy rules to create a new class of weighted fuzzy rules. This study contributes to the advancement of fuzzy modeling and offers a framework for further research and practical applications.

在本文中，我们探讨了一般一元假设自动机量词的使用，并为它们的特定子类提供了表示。此外，我们明确地关注用于分析特定关系依赖的隐含量词。讨论了它们在模糊建模中的适用性，并证明了它们与适当的模糊规则的集成，从而创建了一类新的加权模糊规则。本研究有助于模糊建模的发展，并为进一步的研究和实际应用提供框架。

引用次数: 0