Pub Date : 2025-09-12DOI: 10.1016/j.ijar.2025.109572
Andrey G. Bronevich , Alexander E. Lepskiy
In this paper, we extend the ideas of measuring conflict among belief functions based on solving Kantorovich problems to the case of measuring conflict within a belief function. We consider three possible interpretations of conflict-free information and propose the functionals for measuring conflict, which can be considered as counterparts of known functionals like the auto-conflict measure, the measure of dissonance, and the measure of logical inconsistency.
{"title":"Three types of internal conflict and its measurement in Dempster-Shafer theory","authors":"Andrey G. Bronevich , Alexander E. Lepskiy","doi":"10.1016/j.ijar.2025.109572","DOIUrl":"10.1016/j.ijar.2025.109572","url":null,"abstract":"<div><div>In this paper, we extend the ideas of measuring conflict among belief functions based on solving Kantorovich problems to the case of measuring conflict within a belief function. We consider three possible interpretations of conflict-free information and propose the functionals for measuring conflict, which can be considered as counterparts of known functionals like the auto-conflict measure, the measure of dissonance, and the measure of logical inconsistency.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109572"},"PeriodicalIF":3.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104438","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}
Pub Date : 2025-09-11DOI: 10.1016/j.ijar.2025.109570
Can Pan, Liangxiao Jiang, Shanshan Si
In crowdsourcing learning, label integration algorithms are applied to infer each instance's integrated label from its multiple noisy label set. Recent advancements have demonstrated that worker modeling is an effective approach to improving label integration's performance. In real-world crowdsourced scenarios, however, each worker often annotates a few instances only, leading to insufficient worker modeling. To address this issue, we propose a novel cross-worker joint modeling-based label integration (CJMLI) algorithm. Different from existing algorithms that focus on modeling individual workers solely, CJMLI exploits cross-worker joint modeling to effectively mitigate the impact of insufficient worker modeling. Specifically, we first employ majority voting to get initial integrated labels and then apply them to estimate worker qualities. Subsequently, for each instance, we randomly select a subset of workers to estimate its class membership probabilities and then generate a weighted instance for each class. Next, we use the weighted instances to train a classifier. This process is executed several times to get multiple classifiers. Finally, we use weighted majority voting to fuse their predicted labels to infer the final integrated label of each instance. Extensive experiments demonstrate that CJMLI significantly outperforms all its competitors.
{"title":"Cross-worker joint modeling-based label integration for crowdsourcing","authors":"Can Pan, Liangxiao Jiang, Shanshan Si","doi":"10.1016/j.ijar.2025.109570","DOIUrl":"10.1016/j.ijar.2025.109570","url":null,"abstract":"<div><div>In crowdsourcing learning, label integration algorithms are applied to infer each instance's integrated label from its multiple noisy label set. Recent advancements have demonstrated that worker modeling is an effective approach to improving label integration's performance. In real-world crowdsourced scenarios, however, each worker often annotates a few instances only, leading to insufficient worker modeling. To address this issue, we propose a novel cross-worker joint modeling-based label integration (CJMLI) algorithm. Different from existing algorithms that focus on modeling individual workers solely, CJMLI exploits cross-worker joint modeling to effectively mitigate the impact of insufficient worker modeling. Specifically, we first employ majority voting to get initial integrated labels and then apply them to estimate worker qualities. Subsequently, for each instance, we randomly select a subset of workers to estimate its class membership probabilities and then generate a weighted instance for each class. Next, we use the weighted instances to train a classifier. This process is executed several times to get multiple classifiers. Finally, we use weighted majority voting to fuse their predicted labels to infer the final integrated label of each instance. Extensive experiments demonstrate that CJMLI significantly outperforms all its competitors.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109570"},"PeriodicalIF":3.0,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104297","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}
Pub Date : 2025-09-10DOI: 10.1016/j.ijar.2025.109569
Ruili Guo , Qinghua Zhang , Yunlong Cheng , Ying Yang , Hang Zhong
Most existing generalized multi-scale rough set models (GMRSMs) are based on Pawlak's rough set, which lacks fault tolerance and thus limits their generalization ability. To improve generalization, the variable precision generalized multi-scale rough set model (VPGMRSM) was proposed. However, this model disrupts the monotonicity of the positive region, posing challenges for optimal scale combination (OSC) selection. To address these issues, a monotonic VPGMRSM is proposed in this paper through a two-stage approximation process. The proposed model preserves the monotonicity of the GMRSM and the fault tolerance of the VPGMRSM, and is further applied to OSC selection. First, the non-monotonicity of the positive region in the original VPGMRSM is analyzed. Then, a monotonic VPGMRSM is proposed, whose information measurements are proven to satisfy the monotonicity lacking in the original model. Second, an extended definition of OSC is proposed based on the positive region in the new model, which significantly simplifies and improves the efficiency of the OSC selection process. Third, two OSC selection algorithms are proposed: one based on binary search to find a single OSC, and the other based on three-way decision theory to identify all OSCs. Finally, the experimental results validate the monotonicity of the positive region in the new model and demonstrate that the proposed algorithms are not only suitable for VPGMRSMs, but also effectively reduce the computation time.
{"title":"Optimal scale combination selection based on a monotonic variable precision multi-scale rough set model","authors":"Ruili Guo , Qinghua Zhang , Yunlong Cheng , Ying Yang , Hang Zhong","doi":"10.1016/j.ijar.2025.109569","DOIUrl":"10.1016/j.ijar.2025.109569","url":null,"abstract":"<div><div>Most existing generalized multi-scale rough set models (GMRSMs) are based on Pawlak's rough set, which lacks fault tolerance and thus limits their generalization ability. To improve generalization, the variable precision generalized multi-scale rough set model (VPGMRSM) was proposed. However, this model disrupts the monotonicity of the positive region, posing challenges for optimal scale combination (OSC) selection. To address these issues, a monotonic VPGMRSM is proposed in this paper through a two-stage approximation process. The proposed model preserves the monotonicity of the GMRSM and the fault tolerance of the VPGMRSM, and is further applied to OSC selection. First, the non-monotonicity of the positive region in the original VPGMRSM is analyzed. Then, a monotonic VPGMRSM is proposed, whose information measurements are proven to satisfy the monotonicity lacking in the original model. Second, an extended definition of OSC is proposed based on the positive region in the new model, which significantly simplifies and improves the efficiency of the OSC selection process. Third, two OSC selection algorithms are proposed: one based on binary search to find a single OSC, and the other based on three-way decision theory to identify all OSCs. Finally, the experimental results validate the monotonicity of the positive region in the new model and demonstrate that the proposed algorithms are not only suitable for VPGMRSMs, but also effectively reduce the computation time.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109569"},"PeriodicalIF":3.0,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145044515","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}
Pub Date : 2025-09-10DOI: 10.1016/j.ijar.2025.109568
Hai-Long Yang , Sheng Gao , Zhi-Lian Guo
In the three-way conflict analysis (TWCA), certain core issues lead to the emergence, development, and resolution of conflicts. Issue reduct enables us to concentrate on key issues and more accurately identify the root causes of conflicts. Existing research primarily addresses issue reduct based on complete three-valued situation tables (TSTs), which have certain limitations. This paper discusses the issue reduct in TWCA based on incomplete fuzzy-valued situation tables (IFSTs). First, to deal with incomplete information, we introduce the Social Trust Network (STN) and the K-Nearest Neighbor (KNN) method, employing an iterative weighting method to fill in missing values. Second, by utilizing the matrix representation of relations among agents, we transform the relation matrix into constraint conditions and propose a recursive backtracking algorithm with pruning strategies to calculate conflict, neutrality, alliance, and global reducts. Finally, we use the development plan of the Gansu Provincial Government as a case study to illustrate the model's applicability and advantages through parameter and comparative analysis.
{"title":"Three-way conflict analysis: Issue reduct based on incomplete fuzzy value information","authors":"Hai-Long Yang , Sheng Gao , Zhi-Lian Guo","doi":"10.1016/j.ijar.2025.109568","DOIUrl":"10.1016/j.ijar.2025.109568","url":null,"abstract":"<div><div>In the three-way conflict analysis (TWCA), certain core issues lead to the emergence, development, and resolution of conflicts. Issue reduct enables us to concentrate on key issues and more accurately identify the root causes of conflicts. Existing research primarily addresses issue reduct based on complete three-valued situation tables (TSTs), which have certain limitations. This paper discusses the issue reduct in TWCA based on incomplete fuzzy-valued situation tables (IFSTs). First, to deal with incomplete information, we introduce the Social Trust Network (STN) and the <em>K</em>-Nearest Neighbor (KNN) method, employing an iterative weighting method to fill in missing values. Second, by utilizing the matrix representation of relations among agents, we transform the relation matrix into constraint conditions and propose a recursive backtracking algorithm with pruning strategies to calculate conflict, neutrality, alliance, and global reducts. Finally, we use the development plan of the Gansu Provincial Government as a case study to illustrate the model's applicability and advantages through parameter and comparative analysis.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109568"},"PeriodicalIF":3.0,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104296","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}
A proof for the NP-containment for the probabilistic coherence problem over events represented by formulas of the infinite-valued Łukasiewicz logic was proposed in [1]. The geometric and combinatorial argument to prove that complexity bound contains a mistake that is fixed in the present paper. Actually we present two ways to restore that imprecise claim and, by doing so, we show that the main result of that paper is indeed valid.
{"title":"Unimodular triangulations in Łukasiewicz logic: Complexity bounds of probabilistic coherence","authors":"Tommaso Flaminio , Serafina Lapenta , Sebastiano Napolitano","doi":"10.1016/j.ijar.2025.109565","DOIUrl":"10.1016/j.ijar.2025.109565","url":null,"abstract":"<div><div>A proof for the NP-containment for the probabilistic coherence problem over events represented by formulas of the infinite-valued Łukasiewicz logic was proposed in <span><span>[1]</span></span>. The geometric and combinatorial argument to prove that complexity bound contains a mistake that is fixed in the present paper. Actually we present two ways to restore that imprecise claim and, by doing so, we show that the main result of that paper is indeed valid.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109565"},"PeriodicalIF":3.0,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145044514","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}
Pub Date : 2025-09-08DOI: 10.1016/j.ijar.2025.109566
Wei Li , Xiaolei Wang , Bin Yang
As a generalization of covering, fuzzy β-covering provides a more accurate and practical representation for incomplete information. This paper primarily proposes several fuzzy neighborhood operators based on diverse aggregation functions in an fuzzy β-covering approximation space (FβCAS) and develops a novel TOPSIS method to address the decision-making problem related to user preference factors. First, two classes of fuzzy neighborhood operators are introduced, derived from t-norms, overlap functions and their residual implications in an FβCAS, with their properties thoroughly analyzed. In addition, multiple fuzzy β-coverings are generated from the original fuzzy β-covering, and the classifications of fuzzy neighborhood operators, along with their partial order relationships, are examined. Based on these operators, two kinds of fuzzy β-covering-based rough sets (FβCRS) are established. Finally, an FβCRS-based fuzzy TOPSIS method is developed to evaluate user preference factors for fresh fruit, thereby demonstrating the rationality and feasibility of the proposed approach.
{"title":"Some fuzzy neighborhood operators on fuzzy β-covering approximation space and their application in user preference evaluation","authors":"Wei Li , Xiaolei Wang , Bin Yang","doi":"10.1016/j.ijar.2025.109566","DOIUrl":"10.1016/j.ijar.2025.109566","url":null,"abstract":"<div><div>As a generalization of covering, fuzzy <em>β</em>-covering provides a more accurate and practical representation for incomplete information. This paper primarily proposes several fuzzy neighborhood operators based on diverse aggregation functions in an fuzzy <em>β</em>-covering approximation space (F<em>β</em>CAS) and develops a novel TOPSIS method to address the decision-making problem related to user preference factors. First, two classes of fuzzy neighborhood operators are introduced, derived from <em>t</em>-norms, overlap functions and their residual implications in an F<em>β</em>CAS, with their properties thoroughly analyzed. In addition, multiple fuzzy <em>β</em>-coverings are generated from the original fuzzy <em>β</em>-covering, and the classifications of fuzzy neighborhood operators, along with their partial order relationships, are examined. Based on these operators, two kinds of fuzzy <em>β</em>-covering-based rough sets (F<em>β</em>CRS) are established. Finally, an F<em>β</em>CRS-based fuzzy TOPSIS method is developed to evaluate user preference factors for fresh fruit, thereby demonstrating the rationality and feasibility of the proposed approach.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109566"},"PeriodicalIF":3.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145044513","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}
Pub Date : 2025-09-05DOI: 10.1016/j.ijar.2025.109564
Danyang Wang , Ping Zhu
Network connectivity analysis enables information source tracing and spread regulation in social systems. While existing studies have explored intuitionistic fuzzy rough (IFR) digraphs to address the representation needs of pervasive uncertainties and dual-polarity information in real-world networks, their neglect of connectivity characteristics has limited applicability in information diffusion scenarios. This study breaks through conventional framework and proposes a connectivity-based IFR digraph model, which achieves comprehensive representation of information oppositionality, uncertainty, and propagative characteristic. First, we explore minimum equivalent intuitionistic fuzzy subgraph (MEIFS) and semi-maximum equivalent intuitionistic fuzzy supergraph (SEIFS). MEIFS preserves original strength of connectedness through minimal arc sets, while SEIFS achieves the same objective via redundant arc augmentation. This complementarity provides a mathematical tool for approximating complex networks. Then, a connectivity-based IFR digraph model is established through the synergy of MEIFS and SEIFS. Finally, according to the co-occurrence characteristics of trust and distrust in society, the community detection algorithm and multi-core-node mining method for IFR trust networks are developed. Comparative analysis with three existing methods demonstrates the superiority of the proposed technique in approximate modeling of adversarial information propagation systems.
{"title":"A novel framework for trust network analysis: Connectivity-based intuitionistic fuzzy rough digraph","authors":"Danyang Wang , Ping Zhu","doi":"10.1016/j.ijar.2025.109564","DOIUrl":"10.1016/j.ijar.2025.109564","url":null,"abstract":"<div><div>Network connectivity analysis enables information source tracing and spread regulation in social systems. While existing studies have explored intuitionistic fuzzy rough (IFR) digraphs to address the representation needs of pervasive uncertainties and dual-polarity information in real-world networks, their neglect of connectivity characteristics has limited applicability in information diffusion scenarios. This study breaks through conventional framework and proposes a connectivity-based IFR digraph model, which achieves comprehensive representation of information oppositionality, uncertainty, and propagative characteristic. First, we explore minimum equivalent intuitionistic fuzzy subgraph (MEIFS) and semi-maximum equivalent intuitionistic fuzzy supergraph (SEIFS). MEIFS preserves original strength of connectedness through minimal arc sets, while SEIFS achieves the same objective via redundant arc augmentation. This complementarity provides a mathematical tool for approximating complex networks. Then, a connectivity-based IFR digraph model is established through the synergy of MEIFS and SEIFS. Finally, according to the co-occurrence characteristics of trust and distrust in society, the community detection algorithm and multi-core-node mining method for IFR trust networks are developed. Comparative analysis with three existing methods demonstrates the superiority of the proposed technique in approximate modeling of adversarial information propagation systems.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109564"},"PeriodicalIF":3.0,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019227","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}
Pub Date : 2025-09-05DOI: 10.1016/j.ijar.2025.109571
Silja Renooij, Johan Kwisthout, Janneke H. Bolt
{"title":"Special issue on the Twelfth International Conference on Probabilistic Graphical Models (PGM 2024)","authors":"Silja Renooij, Johan Kwisthout, Janneke H. Bolt","doi":"10.1016/j.ijar.2025.109571","DOIUrl":"10.1016/j.ijar.2025.109571","url":null,"abstract":"","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109571"},"PeriodicalIF":3.0,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010082","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}
Pub Date : 2025-09-03DOI: 10.1016/j.ijar.2025.109567
C. Bender , S.E. Ferrando , K. Gajewski , A.L. González
Supermartingales are here defined in a non-probabilistic setting and can be interpreted solely in terms of superhedging operations. The classical expectation operator is replaced by a pair of subadditive operators: one defines a class of null sets, and the other acts as an outer integral. These operators are motivated by a financial theory of no-arbitrage pricing. Such a setting extends the classical stochastic framework by replacing the path space of the process by a trajectory set, while also providing a financial/gambling interpretation based on the notion of superhedging. The paper proves analogues of the following classical results: Doob's supermartingale decomposition and Doob's pointwise convergence theorem for non-negative supermartingales. The approach shows how linearity of the expectation operator can be circumvented and how integrability properties in the proposed setting lead to the special case of (hedging) martingales while no integrability conditions are required for the general supermartingale case.
{"title":"Superhedging supermartingales","authors":"C. Bender , S.E. Ferrando , K. Gajewski , A.L. González","doi":"10.1016/j.ijar.2025.109567","DOIUrl":"10.1016/j.ijar.2025.109567","url":null,"abstract":"<div><div>Supermartingales are here defined in a non-probabilistic setting and can be interpreted solely in terms of superhedging operations. The classical expectation operator is replaced by a pair of subadditive operators: one defines a class of null sets, and the other acts as an outer integral. These operators are motivated by a financial theory of no-arbitrage pricing. Such a setting extends the classical stochastic framework by replacing the path space of the process by a trajectory set, while also providing a financial/gambling interpretation based on the notion of superhedging. The paper proves analogues of the following classical results: Doob's supermartingale decomposition and Doob's pointwise convergence theorem for non-negative supermartingales. The approach shows how linearity of the expectation operator can be circumvented and how integrability properties in the proposed setting lead to the special case of (hedging) martingales while no integrability conditions are required for the general supermartingale case.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109567"},"PeriodicalIF":3.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010090","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}
Pub Date : 2025-09-01DOI: 10.1016/j.ijar.2025.109550
Eugenio Clerico
We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimality of the coin-betting formulation among e-variable-based algorithmic frameworks for testing and estimating the (conditional) mean. As a consequence, we provide a direct and explicit characterisation of all valid e-variables and e-processes for this testing problem. In the language of classical statistical decision theory, we fully describe the set of all admissible e-variables and e-processes, and identify the corresponding minimal complete class.
{"title":"On the optimality of coin-betting for mean estimation","authors":"Eugenio Clerico","doi":"10.1016/j.ijar.2025.109550","DOIUrl":"10.1016/j.ijar.2025.109550","url":null,"abstract":"<div><div>We consider the problem of testing the mean of a bounded real random variable. We introduce a notion of optimal classes for e-variables and e-processes, and establish the optimality of the coin-betting formulation among e-variable-based algorithmic frameworks for testing and estimating the (conditional) mean. As a consequence, we provide a direct and explicit characterisation of all valid e-variables and e-processes for this testing problem. In the language of classical statistical decision theory, we fully describe the set of all admissible e-variables and e-processes, and identify the corresponding minimal complete class.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109550"},"PeriodicalIF":3.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932346","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}
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