International Journal of Approximate Reasoning最新文献

{"title":"Fuzzy neighborhood components analysis: Supervised dimensionality reduction under uncertain labels","authors":"Mohd Aquib ,&nbsp;Mohd Suhail Naim","doi":"10.1016/j.ijar.2026.109635","DOIUrl":"10.1016/j.ijar.2026.109635","url":null,"abstract":"<div><div>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 <em>k</em>-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 <em>k</em>-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 <em>k</em>NN, 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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"191 ","pages":"Article 109635"},"PeriodicalIF":3.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the edges of characteristic imset polytopes","authors":"Svante Linusson,&nbsp;Petter Restadh,&nbsp;Liam Solus","doi":"10.1016/j.ijar.2025.109606","DOIUrl":"10.1016/j.ijar.2025.109606","url":null,"abstract":"<div><div>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, <span><math><msub><mrow><mrow><mi>C</mi></mrow><mi>I</mi><mi>M</mi></mrow><mi>p</mi></msub></math></span>, can provide a diverse set of such rules. Characterizing the edge graph of <span><math><msub><mrow><mrow><mi>C</mi></mrow><mi>I</mi><mi>M</mi></mrow><mi>p</mi></msub></math></span> is a generally challenging problem. However, many algorithms first estimate the adjacencies in the causal DAG, in the form of an undirected graph <em>G</em>, prior to orienting the edges. In this regime, knowledge of the subpolytope <span><math><msub><mrow><mrow><mi>C</mi></mrow><mi>I</mi><mi>M</mi></mrow><mi>G</mi></msub></math></span> defined for DAGs with adjacencies specified by <em>G</em> is valuable. In this paper, we characterize the edge graph of <span><math><msub><mrow><mrow><mi>C</mi></mrow><mi>I</mi><mi>M</mi></mrow><mi>G</mi></msub></math></span> when <em>G</em> 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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"191 ","pages":"Article 109606"},"PeriodicalIF":3.0,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized fiducial inference on differentiable manifolds","authors":"A.C. Murph ,&nbsp;J.P. Williams ,&nbsp;J. Hannig","doi":"10.1016/j.ijar.2025.109618","DOIUrl":"10.1016/j.ijar.2025.109618","url":null,"abstract":"<div><div>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 <em>constrained generalized fiducial distribution</em> (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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109618"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sweep transform on imaginary matrices and its application to parameter estimation with Gaussian belief functions","authors":"Liping Liu","doi":"10.1016/j.ijar.2025.109607","DOIUrl":"10.1016/j.ijar.2025.109607","url":null,"abstract":"<div><div>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 <em>the sweep transform on imaginary matrices</em>as 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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109607"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Game-theoretic multi-granularity consensus adjustment for social network group decision-making","authors":"Hanzhong Hou ,&nbsp;Chao Zhang ,&nbsp;Deyu Li ,&nbsp;Wentao Li","doi":"10.1016/j.ijar.2025.109610","DOIUrl":"10.1016/j.ijar.2025.109610","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109610"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145735355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Measuring external conflict in Dempster-Shafer theory based on Kantorovich problems","authors":"Andrey G. Bronevich ,&nbsp;Alexander E. Lepskiy","doi":"10.1016/j.ijar.2025.109597","DOIUrl":"10.1016/j.ijar.2025.109597","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109597"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145735356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An axiomatic development of Pereira-Stern e-value as a measure of support for statistical hypotheses","authors":"Yasmin F. Cavaliere,&nbsp;Luís G. Esteves,&nbsp;Victor Fossaluza","doi":"10.1016/j.ijar.2025.109622","DOIUrl":"10.1016/j.ijar.2025.109622","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109622"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Towards a Δ-based metric framework for NMΔ: Δ truth degree and Δ logic metric space","authors":"Bo Wang ,&nbsp;Xiaoquan Xu","doi":"10.1016/j.ijar.2025.109619","DOIUrl":"10.1016/j.ijar.2025.109619","url":null,"abstract":"<div><div>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 <span><math><mrow><mo>(</mo><mi>F</mi><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow><mo>,</mo><msubsup><mi>ρ</mi><mrow><mi>n</mi></mrow><mstyle><mi>Δ</mi></mstyle></msubsup><mo>)</mo></mrow></math></span>. 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 <span><math><msubsup><mi>ρ</mi><mrow><mi>n</mi></mrow><mstyle><mi>Δ</mi></mstyle></msubsup></math></span> 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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109619"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145837495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fuzzy rules with quantifiers as weights","authors":"Martina Daňková ,&nbsp;Dana Hliněná","doi":"10.1016/j.ijar.2025.109600","DOIUrl":"10.1016/j.ijar.2025.109600","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109600"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145665626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New construction of decision evaluation functions on three-way decision spaces based on automorphisms of hesitant fuzzy truth values","authors":"Yuedong Zheng ,&nbsp;Bao Qing Hu ,&nbsp;Guitian He","doi":"10.1016/j.ijar.2025.109620","DOIUrl":"10.1016/j.ijar.2025.109620","url":null,"abstract":"<div><div>As a pivotal theoretical branch of three-way decision (3WD), the concept of Three-way Decision Space (3WDS) effectively unifies 3WD models within fuzzy lattices and other partially ordered sets, providing researchers with a comprehensive information system for 3WD. While various types of 3WDSs have been extensively studied, decision-makers often benefit from a wider array of options to achieve better outcomes. To address this need and enrich the decision-making toolkit, this paper introduces novel construction of decision evaluation functions (DEFs). At first, based on the core axiomatic definitions in 3WDSs- DEF -this paper introduces automorphisms on bounded posets to construct such functions, deriving numerous novel DEFs. The second, this paper proposes new transformation methods from semi-decision evaluation functions (S-DEFs) (resp., quasi-decision evaluation functions (Q-DEFs)) to DEFs, extending the methodological toolkit. And then, this paper investigates the interplay between automorphisms and involution negations on bounded posets, with a focused analysis of their properties in the context of truth value set <span><math><mrow><msup><mn>2</mn><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></msup><mo>−</mo><mrow><mo>{</mo><mi>⌀</mi><mo>}</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"190 ","pages":"Article 109620"},"PeriodicalIF":3.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145880982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}