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}
Pub Date : 2025-08-29DOI: 10.1016/j.ijar.2025.109552
Ziling Ma, Ángel López-Oriona, Hernando Ombao, Ying Sun
Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, showing overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.
{"title":"FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis","authors":"Ziling Ma, Ángel López-Oriona, Hernando Ombao, Ying Sun","doi":"10.1016/j.ijar.2025.109552","DOIUrl":"10.1016/j.ijar.2025.109552","url":null,"abstract":"<div><div>Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption that clusters are sufficiently separated with little overlap. However, real-world data often defy this assumption, showing overlapping distributions or overlapping clouds of points and blurred boundaries between clusters. Fuzzy clustering offers a compelling alternative by allowing partial membership in multiple clusters, making it well-suited for these ambiguous scenarios. Despite its advantages, current fuzzy clustering methods primarily focus on univariate time series, and for multivariate cases, even datasets of moderate dimensionality become computationally prohibitive. This challenge is further exacerbated when dealing with time series of varying lengths, leaving a clear gap in addressing the complexities of modern datasets. This work introduces a novel fuzzy clustering approach based on common principal component analysis to address the aforementioned shortcomings. Our method has the advantage of efficiently handling high-dimensional multivariate time series by reducing dimensionality while preserving critical temporal features. Extensive numerical results show that our proposed clustering method outperforms several existing approaches in the literature. An interesting application involving brain signals from different drivers recorded from a simulated driving experiment illustrates the potential of the approach.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109552"},"PeriodicalIF":3.0,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925197","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 : 2025-08-28DOI: 10.1016/j.ijar.2025.109561
Yigao Li, Weihua Xu
With the development of Rough Set Theory (RST), many improved theories based on RST have emerged. Some of these theories have been applied in the field of feature selection, significantly improving its efficiency. However, they have not yet been widely used in multi-source information domains. This paper proposes a multi-source information fusion method based on Granular-Rectangular Neighborhood Rough Set (GRNRS) and graph theory. First, an improved algorithm based on GRNRS is proposed to evaluate the contribution of each information source to a classification task under a specific attribute. In this process, we provided rigorous theoretical proofs for the concepts and mechanisms used in the improved GRNRS. Meanwhile, the Pearson Correlation Coefficient (PCC) is used to assess the linear relationship between information sources. Then, by integrating the results of the improved GRNRS algorithm and PCC, the adjacency matrix of a graph is constructed. Finally, the preference value of each information source under a specific attribute is calculated based on the adjacency matrix. Information fusion under a specific attribute is achieved by selecting the information source with the highest preference value. Extensive experiments are conducted to analyze the impact of the algorithm's parameters on its final performance. Meanwhile, our method is compared with seven other information fusion algorithms using three metrics: classification accuracy, Average Quality (AQ), and runtime. Friedman and Nemenyi tests are conducted on the comparison results under the classification accuracy and AQ metrics, demonstrating that there are significant differences among the algorithms. The results demonstrate that the proposed algorithm is both time-efficient and effective.
{"title":"Explainable granular fusion: Graph-embedded rectangular neighborhood rough sets for knowledge system convergence","authors":"Yigao Li, Weihua Xu","doi":"10.1016/j.ijar.2025.109561","DOIUrl":"10.1016/j.ijar.2025.109561","url":null,"abstract":"<div><div>With the development of Rough Set Theory (RST), many improved theories based on RST have emerged. Some of these theories have been applied in the field of feature selection, significantly improving its efficiency. However, they have not yet been widely used in multi-source information domains. This paper proposes a multi-source information fusion method based on Granular-Rectangular Neighborhood Rough Set (GRNRS) and graph theory. First, an improved algorithm based on GRNRS is proposed to evaluate the contribution of each information source to a classification task under a specific attribute. In this process, we provided rigorous theoretical proofs for the concepts and mechanisms used in the improved GRNRS. Meanwhile, the Pearson Correlation Coefficient (PCC) is used to assess the linear relationship between information sources. Then, by integrating the results of the improved GRNRS algorithm and PCC, the adjacency matrix of a graph is constructed. Finally, the preference value of each information source under a specific attribute is calculated based on the adjacency matrix. Information fusion under a specific attribute is achieved by selecting the information source with the highest preference value. Extensive experiments are conducted to analyze the impact of the algorithm's parameters on its final performance. Meanwhile, our method is compared with seven other information fusion algorithms using three metrics: classification accuracy, Average Quality (AQ), and runtime. Friedman and Nemenyi tests are conducted on the comparison results under the classification accuracy and AQ metrics, demonstrating that there are significant differences among the algorithms. The results demonstrate that the proposed algorithm is both time-efficient and effective.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109561"},"PeriodicalIF":3.0,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922645","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 : 2025-08-27DOI: 10.1016/j.ijar.2025.109553
Yi Xu , Shujuan Fang , Xuhui Xing
Data missing has always been a challenging problem in machine learning. The Generative Adversarial Imputation Networks (GAIN) have been shown to outperform many existing solutions. However, in GAIN, because missing values lack ground truth as supervision, it is unable to construct reconstruction loss for missing values and can only judge the reasonableness of imputed values based on reconstruction loss of non-missing values and adversarial loss. From the perspective of granular computing, data has levels, and data at different levels of granularity encapsulates different knowledge. Therefore, based on granular computing, this paper proposes a self-supervised multi-level generative adversarial network data imputation algorithm (MGAIN). Firstly, multiple levels of data are constructed using nested feature set sequences. Then, GAIN is used to impute missing values at the coarsest granularity level, and the imputation results of missing values at the coarse granularity level are used as supervision for imputing missing values at the fine granularity level, constructing reconstruction loss for missing values at the fine granularity level. Finally, based on reconstruction loss of missing values, reconstruction loss of non-missing values, and adversarial loss, data at the finer granularity level is imputed. MGAIN imputes missing values level by level from the coarse granularity level to the fine granularity level to obtain more accurate imputation results. Experimental results validate the effectiveness of the proposed method.
{"title":"Self-supervised multi-level generative adversarial network data imputation algorithm","authors":"Yi Xu , Shujuan Fang , Xuhui Xing","doi":"10.1016/j.ijar.2025.109553","DOIUrl":"10.1016/j.ijar.2025.109553","url":null,"abstract":"<div><div>Data missing has always been a challenging problem in machine learning. The Generative Adversarial Imputation Networks (GAIN) have been shown to outperform many existing solutions. However, in GAIN, because missing values lack ground truth as supervision, it is unable to construct reconstruction loss for missing values and can only judge the reasonableness of imputed values based on reconstruction loss of non-missing values and adversarial loss. From the perspective of granular computing, data has levels, and data at different levels of granularity encapsulates different knowledge. Therefore, based on granular computing, this paper proposes a self-supervised multi-level generative adversarial network data imputation algorithm (MGAIN). Firstly, multiple levels of data are constructed using nested feature set sequences. Then, GAIN is used to impute missing values at the coarsest granularity level, and the imputation results of missing values at the coarse granularity level are used as supervision for imputing missing values at the fine granularity level, constructing reconstruction loss for missing values at the fine granularity level. Finally, based on reconstruction loss of missing values, reconstruction loss of non-missing values, and adversarial loss, data at the finer granularity level is imputed. MGAIN imputes missing values level by level from the coarse granularity level to the fine granularity level to obtain more accurate imputation results. Experimental results validate the effectiveness of the proposed method.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109553"},"PeriodicalIF":3.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925202","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 : 2025-08-22DOI: 10.1016/j.ijar.2025.109551
Zhaoqun Li, Beishui Liao, Chen Chen
Probabilistic Argumentation Frameworks (PAFs) extend Abstract Argumentation Frameworks (AAFs) by incorporating probabilistic measures to evaluate argument acceptability. While acceptability evaluations are determined by semantics in both AAFs and PAFs, some key properties underlying semantic behavior in PAFs remain underexplored. This paper systematically investigates directionality, skepticism adequacy, and dynamic monotony in PAFs, establishing their satisfiability across classical semantics. Importantly, we demonstrate that under any semantics, the satisfiability of directionality and skepticism adequacy from the perspective of individual argument acceptability is equivalent between AAFs and PAFs. Besides, for dynamics, we characterize how argument acceptabilities change with structural changes in PAFs, affected by the parity of attack paths. These theoretical insights advance the understanding of argumentation semantics under uncertainty, thereby providing guidance for adapting semantics in probabilistic environments.
{"title":"Investigation of semantic behavior in probabilistic argumentation","authors":"Zhaoqun Li, Beishui Liao, Chen Chen","doi":"10.1016/j.ijar.2025.109551","DOIUrl":"10.1016/j.ijar.2025.109551","url":null,"abstract":"<div><div>Probabilistic Argumentation Frameworks (PAFs) extend Abstract Argumentation Frameworks (AAFs) by incorporating probabilistic measures to evaluate argument acceptability. While acceptability evaluations are determined by semantics in both AAFs and PAFs, some key properties underlying semantic behavior in PAFs remain underexplored. This paper systematically investigates directionality, skepticism adequacy, and dynamic monotony in PAFs, establishing their satisfiability across classical semantics. Importantly, we demonstrate that under any semantics, the satisfiability of directionality and skepticism adequacy from the perspective of individual argument acceptability is equivalent between AAFs and PAFs. Besides, for dynamics, we characterize how argument acceptabilities change with structural changes in PAFs, affected by the parity of attack paths. These theoretical insights advance the understanding of argumentation semantics under uncertainty, thereby providing guidance for adapting semantics in probabilistic environments.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109551"},"PeriodicalIF":3.0,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902151","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 : 2025-08-20DOI: 10.1016/j.ijar.2025.109549
Marco Grzegorczyk
We develop a new Bayesian model to infer the structure of Bayesian networks from hybrid data, that is, data containing a mix of continuous (Gaussian) and discrete (categorical) variables. In line with state-of-the-art hybrid Bayesian network models, we do not allow discrete variables to have continuous parents. However, our new model differs from existing approaches by incorporating discrete variables through multivariate linear regression rather than mixture modeling. In our model, the continuous variables follow a multivariate Gaussian distribution with a shared covariance matrix, while the mean vector varies across different configurations.
As with all Bayesian network models, we use directed acyclic graphs (DAGs) to represent conditional dependency relations among the continuous variables. For our Gaussian distribution, this requires the covariance matrix to be consistent with the structure of the DAG. Our key idea is to apply multivariate linear regression, using the discrete variables as potential covariates to adjust the mean vector of the multivariate Gaussian distribution. Each continuous variable is associated with its own regression model and discrete parent set. Since the values of the discrete variables vary across observations, the mean vector becomes observation-specific.
This enables mean-adjustment of the continuous variables for their discrete parents while simultaneously inferring a Gaussian Bayesian network among them. In simulation studies, we compare our new model against two state-of-the-art hybrid Bayesian network models and demonstrate that both existing models have conceptual shortcomings, positioning our new hybrid Bayesian network model as a strong alternative.
{"title":"Being Bayesian about learning Bayesian networks from hybrid data","authors":"Marco Grzegorczyk","doi":"10.1016/j.ijar.2025.109549","DOIUrl":"10.1016/j.ijar.2025.109549","url":null,"abstract":"<div><div>We develop a new Bayesian model to infer the structure of Bayesian networks from hybrid data, that is, data containing a mix of continuous (Gaussian) and discrete (categorical) variables. In line with state-of-the-art hybrid Bayesian network models, we do not allow discrete variables to have continuous parents. However, our new model differs from existing approaches by incorporating discrete variables through multivariate linear regression rather than mixture modeling. In our model, the continuous variables follow a multivariate Gaussian distribution with a shared covariance matrix, while the mean vector varies across different configurations.</div><div>As with all Bayesian network models, we use directed acyclic graphs (DAGs) to represent conditional dependency relations among the continuous variables. For our Gaussian distribution, this requires the covariance matrix to be consistent with the structure of the DAG. Our key idea is to apply multivariate linear regression, using the discrete variables as potential covariates to adjust the mean vector of the multivariate Gaussian distribution. Each continuous variable is associated with its own regression model and discrete parent set. Since the values of the discrete variables vary across observations, the mean vector becomes observation-specific.</div><div>This enables mean-adjustment of the continuous variables for their discrete parents while simultaneously inferring a Gaussian Bayesian network among them. In simulation studies, we compare our new model against two state-of-the-art hybrid Bayesian network models and demonstrate that both existing models have conceptual shortcomings, positioning our new hybrid Bayesian network model as a strong alternative.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109549"},"PeriodicalIF":3.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886819","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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