International Journal of Approximate Reasoning最新文献_第7页

Optimizing connectivity in fuzzy graphs for resilient disaster response networks 弹性灾害响应网络模糊图连通性优化

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

International Journal of Approximate Reasoning

Pub Date : 2025-07-29 DOI: 10.1016/j.ijar.2025.109535

P Sujithra , Sunil Mathew , J.N. Mordeson

Despite significant technological advances in recent years, communication challenges still persist. These issues are especially evident during crises, where system failures, network overloads, and incompatibilities among the communication technologies used by different organizations create major obstacles. Catastrophe scenarios are marked by high information uncertainty and limited control, which raises challenges for crisis communication. However, these aspects remain underexplored from a network-theoretic perspective. This study investigates the

(x, y)

-connectivity parameter between two nodes in a fuzzy graph, offering insights into network structure, robustness, and performance. We introduce a novel classification of nodes and edges into three categories: enhancing, eroded, and persisting, based on their impact on node-to-node connectivity. The behavior of these classifications is analyzed across different classes of fuzzy graphs. Furthermore, we establish upper and lower bounds for the

(x, y)

-connectivity under two graph operations. An efficient algorithm is proposed to identify and categorize nodes and edges accordingly. The practical relevance of our classification is illustrated through its application to disaster response communication networks, where maintaining resilient and adaptive communication is critical.

尽管近年来取得了重大的技术进步，但通信挑战仍然存在。这些问题在危机期间尤其明显，在危机期间，系统故障、网络过载以及不同组织使用的通信技术之间的不兼容造成了主要障碍。灾难情景具有信息不确定性高、控制有限的特点，给危机沟通带来了挑战。然而，从网络理论的角度来看，这些方面还没有得到充分的探讨。本研究调查了模糊图中两个节点之间的（x,y）连接参数，提供了对网络结构，鲁棒性和性能的见解。基于对节点到节点连通性的影响，我们将节点和边分为三类：增强、侵蚀和持久。在不同类别的模糊图中分析了这些分类的行为。进一步，我们建立了两种图运算下(x,y)-连通性的上界和下界。提出了一种有效的节点和边的识别和分类算法。我们的分类的实际意义是通过它在灾难响应通信网络中的应用来说明的，其中保持弹性和适应性通信是至关重要的。

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引用次数: 0

Generalized conjunction and disjunction of two conditional events in the setting of conditional random quantities 条件随机量下两个条件事件的广义合取与析取

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

International Journal of Approximate Reasoning

Pub Date : 2025-07-28 DOI: 10.1016/j.ijar.2025.109533

Lydia Castronovo , Giuseppe Sanfilippo

In recent papers, notions of conjunction and disjunction of two conditional events as suitable conditional random quantities, which satisfy basic probabilistic properties, have been deepened in the setting of coherence. In this framework, the conjunction and the disjunction of two conditional events are defined as five-valued objects, among which are the values of the (subjectively) assigned probabilities of the two conditional events. In the present paper we propose a generalization of these structures, where these new objects, instead of depending on the probabilities of the two conditional events, depend on two arbitrary values

a, b

in the unit interval. We show that they are connected by a generalized version of the De Morgan's law and, by means of a geometrical approach, we compute the lower and upper bounds on these new objects both in the precise and the imprecise case. Moreover, some particular cases, obtained for specific values of a and b or in case of some logical relations, are analyzed. The results of this paper lead to the conclusion that the only objects satisfying all the logical and the probabilistic properties already valid for the operations between events are the ones depending on the probabilities of the two conditional events.

近年来，在相干性的背景下，深化了两个条件事件作为满足基本概率性质的条件随机量的合取和析取的概念。在该框架中，将两个条件事件的合取和析取定义为五值对象，其中五值对象为两个条件事件（主观）赋值概率的值。在本文中，我们提出了这些结构的推广，其中这些新对象不是依赖于两个条件事件的概率，而是依赖于单位区间内的两个任意值a，b。我们用广义的德摩根定律证明了它们之间的联系，并通过几何方法计算了这些新对象在精确和不精确情况下的下界和上界。此外，还分析了a和b的特定值或某些逻辑关系下的一些特殊情况。本文的结果表明，满足事件间运算所有有效的逻辑和概率性质的对象是依赖于两个条件事件的概率的对象。

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引用次数: 0

Explainable multi-criteria decision-making: A three-way decision perspective 可解释的多准则决策：三向决策视角

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2025-07-18 DOI: 10.1016/j.ijar.2025.109528

Chengjun Shi, Yiyu Yao

This paper proposes an Explainable Multi-Criteria Decision-Making (XMCDM) framework that constructs trilevel explanations with respect to classic multi-criteria decision-making methods. The framework consists of explainable data preparation, explainable decision analysis, and explainable decision support, which integrates ideas from three-way decision and symbols-meaning-value spaces. First, we briefly introduce the key concepts at each level and list potential issues to be resolved, including gathering multi-criteria data, interpreting multi-criteria decision-making working principles, and offering effective outcome presentation. We examine existing literature that solves part of those questions and point out that rule-based explanations may be applicable and efficient to explain ranking/ordering results. Then, we discuss two methods that generate three-way rankings with respect to an individual criterion and integrate three-way rankings with multi-criteria ranking. We modify the Iterative Dichotomiser 3 algorithm to build rule-based explanations. Finally, after giving a small illustrative example, we design experiments on five real-life datasets, test explainability of three classic multi-criteria decision-making methods, and tune the thresholds. The experimental results demonstrate that our proposed framework is feasible and adaptable to various data characteristics.

本文提出了一个可解释的多准则决策（XMCDM）框架，该框架针对经典的多准则决策方法构建了三级解释。该框架由可解释的数据准备、可解释的决策分析和可解释的决策支持组成，融合了三方决策和符号-意义-价值空间的思想。首先，我们简要介绍了每个级别的关键概念，并列出了需要解决的潜在问题，包括收集多标准数据，解释多标准决策工作原理，以及提供有效的结果展示。我们研究了解决这些问题的现有文献，并指出基于规则的解释可能适用且有效地解释排名/排序结果。然后，我们讨论了基于单个标准生成三向排名的两种方法，并将三向排名与多标准排名相结合。我们修改了迭代二分器3算法来构建基于规则的解释。最后，在给出一个小示例后，我们在五个实际数据集上设计了实验，测试了三种经典多准则决策方法的可解释性，并调整了阈值。实验结果表明，该框架是可行的，并能适应各种数据特征。

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引用次数: 0

Fusing fuzzy rough sets and mean shift for anomaly detection 基于模糊粗糙集和均值移位的异常检测

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

International Journal of Approximate Reasoning

Pub Date : 2025-07-18 DOI: 10.1016/j.ijar.2025.109530

Mengyao Liao , Zhiyu Chen , Can Gao , Jie Zhou , Xiaodong Yue

Outlier detection is a critical but challenging task due to the complex distribution of practical data, and some Fuzzy Rough Sets (FRS)-based methods have been presented to identify outliers from these data. However, these methods still have limitations when facing the co-existence of different types of outliers. In this study, an improved FRS-based unsupervised anomaly detection method is proposed by integrating distance and density information. Specifically, to detect the local outliers, a fuzzy granule density is first defined by introducing a Gaussian kernel similarity to characterize the local density of samples. Then, optimistic and pessimistic fuzzy granule densities are further developed to evaluate the density variation in the local neighborhood. Moreover, a distance measure based on mean shift is introduced to detect global and group outliers. Finally, an outlier detection method that integrates the density and distance measures is designed to effectively identify diverse types of outliers. Extensive experiments on synthetic and public datasets, along with statistical significance analysis, demonstrate the superior performance of the proposed method, achieving an average improvement of at least 12.27% in terms of AUROC.

由于实际数据的复杂分布，异常值检测是一项关键但具有挑战性的任务，一些基于模糊粗糙集（FRS）的方法已经提出了从这些数据中识别异常值的方法。然而，这些方法在面对不同类型离群值共存时仍然存在局限性。本文提出了一种改进的基于frs的无监督异常检测方法，将距离和密度信息相结合。具体来说，为了检测局部异常值，首先通过引入高斯核相似度来定义模糊颗粒密度来表征样本的局部密度。然后，进一步发展乐观和悲观模糊颗粒密度来评价局部邻域的密度变化。此外，还引入了一种基于均值位移的距离度量来检测全局异常点和组异常点。最后，设计了一种融合密度和距离测度的离群点检测方法，有效识别不同类型的离群点。在合成和公共数据集上进行的大量实验以及统计显著性分析表明，所提出的方法具有优越的性能，在AUROC方面平均提高了至少12.27%。

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引用次数: 0

Maximal consistent blocks-based optimistic and pessimistic probabilistic rough fuzzy sets and their applications in three-way multiple attribute decision-making 基于最大一致块的乐观和悲观概率粗糙模糊集及其在三向多属性决策中的应用

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2025-07-17 DOI: 10.1016/j.ijar.2025.109529

Yan Sun , Bin Pang , Ju-Sheng Mi , Wei-Zhi Wu

The integration of three-way decision (3WD) into multiple attribute decision-making (MADM) problems has emerged as a pivotal research area. 3WD can effectively manage the inherent uncertainty within the decision-making process. Additionally, it offers a semantic interpretation of the outcomes. In this paper, we introduce two innovative 3WD-MADM approaches, with a focus on granule selection and the handling of multi-type information in the framework of three-way decisions. Firstly, we construct maximal consistent blocks (MCBs)-based pessimistic and optimistic probabilistic rough fuzzy set (RFS) models and investigate their properties to ascertain their efficacy and reliability in decision-making contexts. Then, we define relative loss functions associated with “good state” and “bad state” scenarios. Building on this, we introduce four types of 3WDs based on our newly proposed optimistic and pessimistic probabilistic RFSs. Furthermore, we integrate the 3WDs information from both scenarios to formulate optimistic and pessimistic 3WD-MADM approaches, handling both single-valued fuzzy and intuitionistic fuzzy information. Finally, we contrast our proposed methodologies with the current MADM methods, and demonstrate their validity, significance and generalization ability.

将三向决策（three-way decision, 3WD）整合到多属性决策（MADM）问题中已经成为一个关键的研究领域。3WD可以有效管理决策过程中固有的不确定性。此外，它还提供了结果的语义解释。在本文中，我们介绍了两种创新的3WD-MADM方法，重点关注颗粒选择和在三方决策框架下多类型信息的处理。首先，构建了基于最大一致块（mcb）的悲观和乐观概率粗糙模糊集（RFS）模型，并研究了它们的性质，以确定它们在决策环境中的有效性和可靠性。然后，我们定义了与“好状态”和“坏状态”场景相关的相对损失函数。在此基础上，我们介绍了基于我们新提出的乐观和悲观概率rfs的四种类型的3wd。在此基础上，我们将两种场景下的3wd信息进行整合，形成乐观和悲观的3WD-MADM方法，分别处理单值模糊信息和直觉模糊信息。最后，我们将所提出的方法与现有的MADM方法进行了对比，验证了其有效性、显著性和泛化能力。

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引用次数: 0

Centralized ordered weighted averaging operator weights and their properties 集中有序加权平均算子权值及其性质

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2025-07-16 DOI: 10.1016/j.ijar.2025.109477

Byeong Seok Ahn

We propose a method for generating ordered weighted averaging (OWA) operator weights based on a preference order expressed through a set of inequalities representing the relative importance of criteria. The resulting centralized OWA (COWA) operator weights are: (i) computationally derived by averaging the coordinates of the extreme points of the feasible set; (ii) mathematically defined as the weights that minimize the sum of squared deviations from each extreme point; (iii) geometrically located at the center of the feasible region defined by the inequalities.

Moreover, for several sets of inequalities, the COWA operator weights closely resemble those of the maximum entropy OWA operator and consistently exhibit a constant attitudinal character (AC), regardless of the number of criteria.

For validation purposes, we introduce a method for generating COWA operator weights that satisfy a specified AC, and demonstrate their similarity to the maximum entropy OWA operator weights through sample tests with varying number of criteria and AC values. The strength of the preference order associated with a specific AC provides deeper insight into how the AC relates to the ordinal relationships among the criteria.

我们提出了一种生成有序加权平均（OWA）算子权重的方法，该方法基于通过一组表示标准相对重要性的不等式表示的优先顺序。得到的集中式OWA （COWA）算子权重为：(i)通过计算求得可行集极值点坐标的平均值；（ii）在数学上定义为使每个极值点的偏差平方和最小的权重；（iii）几何上位于由不等式定义的可行区域的中心。此外，对于一些不等式集，COWA算子的权重与最大熵OWA算子的权重非常相似，并且无论标准的数量如何，都始终表现出恒定的态度特征（AC）。为了验证目的，我们引入了一种方法来生成满足指定AC的COWA算子权重，并通过具有不同数量的标准和AC值的样本测试来证明它们与最大熵OWA算子权重的相似性。与特定AC相关联的偏好顺序的强度可以更深入地了解AC如何与标准之间的顺序关系相关联。

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引用次数: 0

Fuzzy sequential three-way multi-scale attribute decision-making method based on individual risk attitude and multi classification features 基于个体风险态度和多分类特征的模糊序列三尺度属性决策方法

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2025-07-15 DOI: 10.1016/j.ijar.2025.109525

Jin Qian , Yuehua Lu , Ying Yu , Di Wang

Multi-attribute decision-making research is of great significance for solving macro problems. However, the existing multi-attribute decision-making methods face two problems: one is how to comprehensively consider the impact of irrational behavior on the decision-making results; the other is how to make intelligent decisions on the evaluation information of “multi-level, multi-classification, multi-perspective”. To address the above two issues, this paper establishes a fuzzy sequential three-way multi-scale attribute decision-making method based on individual risk attitudes and multi-classification features. First, we construct multiple attribute combinations from the inconsistent multi-scale attribute set and weight and aggregate them into comprehensive decision attributes, thereby transforming them from multi-scale to multi-view. Next, we identify multiple attribute clusters through hierarchical clustering and create a class-cluster dependency definition to determine the sequential set using a heuristic algorithm. We then propose a specific sequential three-way decision model within the framework of granular computing, tailored to the characteristics of the evaluation information. For object ranking, we pre-rank the objects based on regret theory and develop two methods to determine category weights based on the classification results obtained from the three-way decision. The stability and effectiveness of the proposed method are verified through corresponding experiments and comparative analysis of real cases.

多属性决策研究对于解决宏观问题具有重要意义。然而，现有的多属性决策方法面临着两个问题：一是如何综合考虑非理性行为对决策结果的影响；二是如何对“多层次、多分类、多视角”的评价信息进行智能决策。针对上述两个问题，本文建立了一种基于个体风险态度和多分类特征的模糊序列三向多尺度属性决策方法。首先，将不一致的多尺度属性集和权值构造多个属性组合，并将其聚合为综合决策属性，从而实现多尺度向多视角的转化；接下来，我们通过分层聚类识别多个属性簇，并创建类-簇依赖定义，以使用启发式算法确定顺序集。然后，根据评价信息的特点，在颗粒计算框架内提出了一个具体的顺序三向决策模型。在对象排序方面，我们基于后悔理论对对象进行预排序，并根据三向决策得到的分类结果，提出了两种确定类别权重的方法。通过相应的实验和实际案例对比分析，验证了所提方法的稳定性和有效性。

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引用次数: 0

Cooperative games with fuzzy characteristic functions on concept lattices 概念格上具有模糊特征函数的合作对策

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2025-07-14 DOI: 10.1016/j.ijar.2025.109527

Martin Waffo Kemgne , Blaise Bleriot Koguep Njionou , Dmitry I. Ignatov , Leonard Kwuida

This paper introduces cooperative games with transferable utilities and fuzzy characteristic functions on concept lattices. While previous works have independently addressed games with fuzzy payoffs and games restricted to structured coalition systems such as lattices, our approach combines both perspectives. We consider cooperative settings where coalition formation is constrained by a concept lattice structure, and the payoff for each feasible coalition is uncertain and represented by a fuzzy quantity. We define a generalized Shapley value for such games, extending previous characterizations proposed for fuzzy games and lattice-structured games. We also provide an axiomatic characterization of this value and illustrate its applicability through a practical example.

引入了具有可转移效用的合作对策和概念格上的模糊特征函数。虽然以前的工作独立地解决了具有模糊收益的博弈和限制于结构化联盟系统（如格子）的博弈，但我们的方法结合了这两种观点。我们考虑了联盟形成受概念格结构约束的合作设置，每个可行联盟的收益是不确定的，用模糊量表示。我们为这种博弈定义了一个广义的Shapley值，扩展了之前提出的模糊博弈和格结构博弈的特征。我们还提供了这个值的一个公理化表征，并通过一个实际例子说明了它的适用性。

引用次数: 0

Cut-elimination theorems for some logics associated with double Stone algebras 双斯通代数相关逻辑的切消定理

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2025-07-09 DOI: 10.1016/j.ijar.2025.109526

Martín Figallo, Juan S. Slagter

A double Stone algebra is a Stone algebra whose dual lattice is also a Stone algebra. Logics that may be associated with double Stone algebras are based on bounded distributive lattices which are endowed with two negations: a Heyting negation (the pseudocomplement) and a Brouwer negation (the dual pseudocomplement) possibly satisfying some constraints. Different authors have studied the order-preserving logic associated with double Stone algebras. Recently, the four-valued character of this logic was exploited by providing a rough set semantics for it.

In this paper, we explore the proof-theoretical aspect of two logics associated with double Stone algebras, namely, the truth-preserving and the order-preserving logic, respectively. We provide sequent systems sound and complete for these logics and prove the cut-elimination theorem for both systems.

双斯通代数是一种斯通代数，它的对偶格也是一种斯通代数。可能与双斯通代数相关的逻辑是基于有界分配格的，这些有界分配格被赋予两个否定：一个Heyting否定（伪补）和一个browwer否定（对偶伪补），可能满足某些约束。不同的作者研究了与双斯通代数相关的保序逻辑。最近，通过为该逻辑提供粗糙集语义，利用了该逻辑的四值特性。在本文中，我们分别探讨了与双石代数相关的两种逻辑的证明理论方面，即保真逻辑和保序逻辑。我们为这些逻辑提供了完备的序系统，并证明了它们的切消定理。

引用次数: 0

Stable structure learning with HC-Stable and Tabu-Stable algorithms HC-Stable和Tabu-Stable算法的稳定结构学习

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning

Pub Date : 2025-07-07 DOI: 10.1016/j.ijar.2025.109522

Neville K. Kitson, Anthony C. Constantinou

Many Bayesian Network structure learning algorithms are unstable, with the learned graph sensitive to arbitrary dataset artifacts, such as the ordering of columns (i.e., variable order). PC-Stable [1] attempts to address this issue for the widely-used PC algorithm, prompting researchers to use the ‘stable’ version instead. However, this problem seems to have been overlooked for score-based algorithms. In this study, we show that some widely-used score-based algorithms, as well as hybrid and constraint-based algorithms, including PC-Stable, suffer from the same issue. We propose a novel solution for score-based greedy hill-climbing that eliminates instability by determining a stable node order, leading to consistent results regardless of variable ordering. The new Tabu-Stable algorithms achieve the highest overall performance in terms of mean BIC score, log-likelihood, and structural accuracy across networks. These results highlight the importance of addressing instability in structure learning and provide a robust and practical approach for future applications. This paper extends the scope and impact of our previous work presented at Probabilistic Graphical Models 2024 [2] by incorporating continuous variables, implementing new stable orders that improve performance further, and demonstrating that the approach remains effective in the presence of sampling noise. The implementations, along with usage instructions, are freely available on GitHub at https://github.com/causal-iq/discovery.

许多贝叶斯网络结构学习算法是不稳定的，学习到的图对任意数据集工件敏感，例如列的顺序（即变量顺序）。PC- stable[1]试图为广泛使用的PC算法解决这个问题，这促使研究人员转而使用“稳定”版本。然而，这个问题似乎被基于分数的算法所忽视。在本研究中，我们证明了一些广泛使用的基于分数的算法，以及混合和基于约束的算法，包括PC-Stable，都存在同样的问题。我们提出了一种基于分数的贪婪爬坡的新解决方案，通过确定稳定的节点顺序来消除不稳定性，从而导致无论变量顺序如何结果一致。新的Tabu-Stable算法在平均BIC分数、对数似然和跨网络的结构精度方面实现了最高的总体性能。这些结果强调了解决结构学习中不稳定性的重要性，并为未来的应用提供了一个强大而实用的方法。本文扩展了我们之前在概率图形模型2024[2]上提出的工作的范围和影响，通过合并连续变量，实现进一步提高性能的新稳定顺序，并证明该方法在存在采样噪声的情况下仍然有效。实现以及使用说明可以在GitHub上免费获得https://github.com/causal-iq/discovery。

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引用次数: 0