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

Three-way conflict analysis: From single-level to multi-level preferences 三向冲突分析：从单一层次偏好到多层次偏好

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

International Journal of Approximate Reasoning

Pub Date : 2025-12-22 DOI: 10.1016/j.ijar.2025.109621

Guangming Lang , Haojun Liu , Mengjun Hu

In three-way conflict analysis, a key challenge lies in faithfully capturing agents’ attitudes towards multiple issues within complex conflict situations. Preference-based conflict situations, which characterize comparisons through ordered issue pairs, offer a structured alternative to traditional rating scales by emphasizing relational judgments. However, existing single-level preference frameworks are limited in their ability to capture variations in preference strengths, confidence levels across agents, and refinements that emerge over time. Moreover, they do not reliably support cross-agent comparison of preference relations. Consequently, single-level models exhibit inherent constraints when representing diverse agent viewpoints across different issue pairs. To overcome these limitations, this paper introduces a multi-level preference framework that generalizes single-level preference, converse, and indifference relations by incorporating multiple levels of relational intensity, thereby enabling a more fine-grained characterization of agents’ preference strengths over issue pairs. Within this framework, we define conflict measures for individual issue pairs between two agents, and further extend them to a set of issues, facilitating the exact quantification of conflict degrees between two agents across multiple issues, and enabling a more accurate trisection of agent pairs into alliance, neutrality, and conflict relations. As a concrete instantiation, we develop a two-level preference-based model distinguishing strong and weak relations, and apply it to a case study on development planning in Gansu Province. A comparative analysis demonstrates that the multi-level preference framework not only captures conflicts with greater expressiveness and accuracy than single-level approaches but also yields richer and more actionable insights for conflict resolution, thereby enhancing both the interpretability and the practical value of three-way conflict analysis.

在三方冲突分析中，一个关键的挑战在于忠实地捕捉agent对复杂冲突情境中多个问题的态度。基于偏好的冲突情境通过有序的问题对进行比较，通过强调关系判断，为传统评级量表提供了一种结构化的替代方案。然而，现有的单级偏好框架在捕捉偏好强度变化、跨代理的置信度以及随着时间的推移而出现的改进方面受到限制。此外，它们不能可靠地支持偏好关系的跨代理比较。因此，单级模型在表示跨不同问题对的不同代理观点时表现出固有的约束。为了克服这些限制，本文引入了一个多层次偏好框架，该框架通过结合多个层次的关系强度来概括单级偏好、反向和无差异关系，从而能够更细粒度地表征代理对问题对的偏好强度。在此框架内，我们定义了两个主体之间单个问题对的冲突度量，并进一步将其扩展到一组问题，从而便于准确量化两个主体之间跨多个问题的冲突程度，并能够更准确地将代理对划分为联盟关系、中立关系和冲突关系。作为具体实例，本文建立了基于偏好的强弱关系两级区分模型，并将其应用于甘肃省发展规划的案例研究。对比分析表明，多层次偏好框架不仅比单层次方法更能表达和准确地捕捉冲突，而且为解决冲突提供了更丰富和更具可操作性的见解，从而提高了三方冲突分析的可解释性和实用价值。

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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 : 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

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 : 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

Weighted feature graph-based multilabel feature selection via multi-metrics with global–local correlation 基于全局-局部相关的多指标加权特征图的多标签特征选择

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

International Journal of Approximate Reasoning

Pub Date : 2025-12-18 DOI: 10.1016/j.ijar.2025.109623

Lin Sun , Changwu Feng , Xiankun Zhang , Jiucheng Xu

Due to the increasing prevalence of multilabel data, multilabel classification must tackle the challenges of high-dimensional feature spaces, complex label dependencies, and sample sparsity, which restricts the effectiveness of multilabel learning. To address these challenges, this work constructs a weighted feature graph-based multilabel feature selection methodology via multi-metrics with global–local correlation. First, fuzzy similarity relations in feature space and fuzzy decision similarity within label space are calculated. A joint fuzzy similarity relation is then constructed to capture the consistency of samples across both spaces. Next, we derive associativity from the joint fuzzy similarity relation, obtain redundancy from the fuzzy similarity relation, and measure interactivity using the fuzzy dependency degree of feature subsets. These three metrics are combined to define the edge weights of the feature graph, thereby describing the complex correlations among features for multilabel classification. Second, to evaluate the global–local correlation, a ridge regression coefficient matrix is presented. Concurrently, the correlation weight of information energy ratio is calculated via mutual information between features and labels, forming a feature-label correlation matrix. We then use a multi-Criteria Decision-Making (MCDM) framework to balance these global and local correlations. This allows us to develop a weighted feature-label matrix and a relative closeness degree for each alternative, which determines the node weights of the weighted feature graph. Third, to dynamically adjust the intensity of information propagation between features, a feature-driven, attention-based weight allocation strategy is studied. We construct a feature node matrix that represents multi-source information fusion and an attention matrix by combining graph structural features with the MCDM results. These are used to form a feature-aware hybrid adjacency matrix. An improved PageRank scheme then iteratively updates the feature ranking scores on this hybrid structure, to select a discriminative and representative feature subset. Experiments illustrate that our methodology outperforms other comparative approaches across several metrics on high-dimensional multilabel data.

由于多标签数据的日益普及，多标签分类必须解决高维特征空间、复杂标签依赖和样本稀疏性等问题，这些问题限制了多标签学习的有效性。为了解决这些问题，本文构建了一种基于加权特征图的多标签特征选择方法，该方法采用全局-局部相关的多指标。首先，计算特征空间中的模糊相似关系和标签空间中的模糊决策相似关系。然后构造一个联合模糊相似关系来捕获两个空间中样本的一致性。其次，从联合模糊相似关系中导出关联性，从模糊相似关系中获得冗余，并利用特征子集的模糊依赖度度量交互性。将这三个指标结合起来定义特征图的边缘权重，从而描述特征之间的复杂关联，用于多标签分类。其次，为了评估全局与局部的相关性，提出了脊回归系数矩阵。同时，通过特征与标签之间的互信息计算信息能量比的相关权重，形成特征-标签相关矩阵。然后，我们使用多标准决策（MCDM）框架来平衡这些全局和局部相关性。这允许我们开发一个加权特征标签矩阵和每个选项的相对接近度，这决定了加权特征图的节点权重。第三，为了动态调整特征之间的信息传播强度，研究了一种特征驱动、基于注意力的权重分配策略。将图结构特征与MCDM结果相结合，构造了表示多源信息融合的特征节点矩阵和注意矩阵。这些被用来形成一个特征感知的混合邻接矩阵。然后，改进的PageRank方案迭代更新该混合结构上的特征排名分数，以选择具有判别性和代表性的特征子集。实验表明，我们的方法在高维多标签数据的几个指标上优于其他比较方法。

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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 : 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

Data speak but sometimes lie: A game-theoretic approach to data bias and algorithmic fairness 数据说话，但有时撒谎：数据偏见和算法公平性的博弈论方法

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

International Journal of Approximate Reasoning

Pub Date : 2025-12-06 DOI: 10.1016/j.ijar.2025.109608

Chiara Manganini, Esther Anna Corsi, Giuseppe Primiero

In the present work, we develop a novel information-theoretic and logic-based approach to data bias in Machine Learning predictions and show its relevance in the specific context of fairness evaluation. We frame predictions made on biased data as Ulam games, which formalise key aspects of data-driven inference, and from which a variation of the rational non-monotonic consequence relation can be defined. We investigate this framework to model how differential levels of noise in input features impact Machine Learning predictions. To the best of our knowledge, this is the first game-theoretic formalisation of ML unfairness.

在目前的工作中，我们开发了一种新的基于信息理论和逻辑的方法来处理机器学习预测中的数据偏差，并展示了其在公平评估的特定背景下的相关性。我们将对有偏差数据的预测框架为Ulam博弈，它形式化了数据驱动推理的关键方面，并从中定义了理性非单调结果关系的变化。我们研究了这个框架，以模拟输入特征中的不同噪声水平如何影响机器学习预测。据我们所知，这是ML不公平的第一个博弈论形式化。

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 : 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

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 : 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

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 : 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

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 : 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