Based on the intuitive idea that sets of objects or entities can be categorized in very different ways, and that some ways to categorise objects are better than others, depending on the purpose of the categorization, in this paper, a formal framework is introduced for parametrically generating a space of possible categorizations of a set of objects, based on the features which individual agents or groups thereof regard as relevant (formally encoded in the notion of interrogative agenda). This formal framework accounts both for two-valued (crisp), and for many-valued (fuzzy) judgments about the relevance of given features, and introduces ways to aggregate individual agendas to group agendas. As an application on this framework, we discuss a machine-learning meta-algorithm for outlier detection and classification which provides local and global explanations of its results.
{"title":"Flexible categorization using formal concept analysis and Dempster-Shafer theory","authors":"Marcel Boersma , Krishna Manoorkar , Alessandra Palmigiano , Mattia Panettiere , Apostolos Tzimoulis , Nachoem Wijnberg","doi":"10.1016/j.ijar.2025.109548","DOIUrl":"10.1016/j.ijar.2025.109548","url":null,"abstract":"<div><div>Based on the intuitive idea that sets of objects or entities can be categorized in very different ways, and that some ways to categorise objects are better than others, depending on the purpose of the categorization, in this paper, a formal framework is introduced for parametrically generating a space of possible categorizations of a set of objects, based on the features which individual agents or groups thereof regard as relevant (formally encoded in the notion of <em>interrogative agenda</em>). This formal framework accounts both for two-valued (crisp), and for many-valued (fuzzy) judgments about the relevance of given features, and introduces ways to aggregate individual agendas to group agendas. As an application on this framework, we discuss a machine-learning meta-algorithm for outlier detection and classification which provides local and global explanations of its results.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109548"},"PeriodicalIF":3.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829502","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}
Triadic Concept Analysis (TCA) is an extension of Formal Concept Analysis (FCA) for handling data represented as a set of objects described by attributes and conditions via a ternary relation. However, the intuition to go from FCA to TCA is not always straightforward. In this paper we discuss some FCA notions from dyadic to triadic. Although some ideas admit straightforward adaptation, most do not. In particular, we address the representation problem, the notion of redundant attributes and subcontexts in the triadic setting.
{"title":"Triadic data: Representation and reduction","authors":"Léa Aubin Kouankam Djouohou , Blaise Blériot Koguep Njionou , Leonard Kwuida","doi":"10.1016/j.ijar.2025.109532","DOIUrl":"10.1016/j.ijar.2025.109532","url":null,"abstract":"<div><div>Triadic Concept Analysis (TCA) is an extension of Formal Concept Analysis (FCA) for handling data represented as a set of objects described by attributes and conditions via a ternary relation. However, the intuition to go from FCA to TCA is not always straightforward. In this paper we discuss some FCA notions from dyadic to triadic. Although some ideas admit straightforward adaptation, most do not. In particular, we address the representation problem, the notion of redundant attributes and subcontexts in the triadic setting.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109532"},"PeriodicalIF":3.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749556","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 : 2025-12-01Epub Date: 2025-08-06DOI: 10.1016/j.ijar.2025.109538
Hongpeng Tian , Zuowei Zhang , Zhunga Liu , Jingwei Zuo , Caixing Yang
Over-sampling methods concentrate on creating balanced samples and have proven successful in classifying imbalanced data. However, current over-sampling methods fail to consider the uncertainty of produced samples, potentially altering the data distribution and impacting the classification process. To address this issue, we propose a distribution assessment-based multiple over-sampling (DAMO) method for classifying imbalanced data. We first introduce a multiple over-sampling method based on distribution assessment to create different forms of synthetic samples. The core is quantifying the inconsistency of data distribution before and after sampling as a constraint to guide multiple over-sampling, thereby minimizing the data shift and characterizing the uncertainty of produced samples. Then, we quantify the local reliability of the classification results and select several imprecise samples with low local reliability that are indistinguishable between classes. Neighbors serve as additional complementary information to calibrate the results of imprecise samples, thereby reducing the likelihood of misclassification. The calibrated results are combined by the discounting Dempster-Shafer fusion rule to make a final decision. DAMO's efficiency has been demonstrated through comparisons with related methods on various real imbalanced datasets.
{"title":"Distribution assessment-based multiple over-sampling with evidence fusion for imbalanced data classification","authors":"Hongpeng Tian , Zuowei Zhang , Zhunga Liu , Jingwei Zuo , Caixing Yang","doi":"10.1016/j.ijar.2025.109538","DOIUrl":"10.1016/j.ijar.2025.109538","url":null,"abstract":"<div><div>Over-sampling methods concentrate on creating balanced samples and have proven successful in classifying imbalanced data. However, current over-sampling methods fail to consider the uncertainty of produced samples, potentially altering the data distribution and impacting the classification process. To address this issue, we propose a distribution assessment-based multiple over-sampling (DAMO) method for classifying imbalanced data. We first introduce a multiple over-sampling method based on distribution assessment to create different forms of synthetic samples. The core is quantifying the inconsistency of data distribution before and after sampling as a constraint to guide multiple over-sampling, thereby minimizing the data shift and characterizing the uncertainty of produced samples. Then, we quantify the local reliability of the classification results and select several imprecise samples with low local reliability that are indistinguishable between classes. Neighbors serve as additional complementary information to calibrate the results of imprecise samples, thereby reducing the likelihood of misclassification. The calibrated results are combined by the discounting Dempster-Shafer fusion rule to make a final decision. DAMO's efficiency has been demonstrated through comparisons with related methods on various real imbalanced datasets.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109538"},"PeriodicalIF":3.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829501","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 : 2025-12-01Epub 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":"2025-12-01","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 : 2025-12-01Epub Date: 2025-07-29DOI: 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 -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 -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.
{"title":"Optimizing connectivity in fuzzy graphs for resilient disaster response networks","authors":"P Sujithra , Sunil Mathew , J.N. Mordeson","doi":"10.1016/j.ijar.2025.109535","DOIUrl":"10.1016/j.ijar.2025.109535","url":null,"abstract":"<div><div>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 <span><math><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span>-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 <span><math><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span>-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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109535"},"PeriodicalIF":3.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749555","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 : 2025-12-01Epub Date: 2025-07-18DOI: 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.
{"title":"Explainable multi-criteria decision-making: A three-way decision perspective","authors":"Chengjun Shi, Yiyu Yao","doi":"10.1016/j.ijar.2025.109528","DOIUrl":"10.1016/j.ijar.2025.109528","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109528"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696896","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 : 2025-12-01Epub Date: 2025-07-30DOI: 10.1016/j.ijar.2025.109531
Sourabh Balgi , Marc Braun , Jose M. Peña , Adel Daoud
We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term ρ-GNF, where is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcome due to unobserved confounding, which is modeled as a Gaussian copula. In other words, the ρ-GNF enables scholars to estimate the average causal effect (ACE) as a function of ρ, accounting for various confounding strengths. The output of the ρ-GNF is what we term the , which provides the bounds for the ACE given an interval of assumed ρ values. The also enables scholars to identify the confounding strength required to nullify the ACE. We also propose a Bayesian version of our sensitivity analysis method. Assuming a prior over the sensitivity parameter ρ enables us to derive the posterior distribution over the ACE, which enables us to derive credible intervals. Finally, leveraging on experiments from simulated and real-world data, we show the benefits of our sensitivity analysis method.
{"title":"Sensitivity analysis to unobserved confounding with copula-based normalizing flows","authors":"Sourabh Balgi , Marc Braun , Jose M. Peña , Adel Daoud","doi":"10.1016/j.ijar.2025.109531","DOIUrl":"10.1016/j.ijar.2025.109531","url":null,"abstract":"<div><div>We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term <em>ρ</em>-GNF, where <span><math><mi>ρ</mi><mo>∈</mo><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>+</mo><mn>1</mn><mo>]</mo></math></span> is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcome due to unobserved confounding, which is modeled as a Gaussian copula. In other words, the <em>ρ</em>-GNF enables scholars to estimate the average causal effect (ACE) as a function of <em>ρ</em>, accounting for various confounding strengths. The output of the <em>ρ</em>-GNF is what we term the <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>c</mi><mi>u</mi><mi>r</mi><mi>v</mi><mi>e</mi></mrow></msub></math></span>, which provides the bounds for the ACE given an interval of assumed <em>ρ</em> values. The <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>c</mi><mi>u</mi><mi>r</mi><mi>v</mi><mi>e</mi></mrow></msub></math></span> also enables scholars to identify the confounding strength required to nullify the ACE. We also propose a Bayesian version of our sensitivity analysis method. Assuming a prior over the sensitivity parameter <em>ρ</em> enables us to derive the posterior distribution over the ACE, which enables us to derive credible intervals. Finally, leveraging on experiments from simulated and real-world data, we show the benefits of our sensitivity analysis method.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109531"},"PeriodicalIF":3.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810435","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 : 2025-12-01Epub Date: 2025-09-12DOI: 10.1016/j.ijar.2025.109573
Huilai Zhi , Qing Wan , Ting Qian , Yinan Li , Jiang Yang
3-valued formal contexts are abstracted from various types of applications such as incomplete formal context based data mining, shadow sets based knowledge discovery and conflict analysis. 3-valued formal contexts differ from binary-valued formal contexts in many aspects, and many distinguished details have not been investigated. To this end, some of the most important properties of 3-valued formal contexts are systematically explored in a cognitive viewpoint based on formal concept analysis. At first, 3-valued concept lattices and formal concept lattices are compared from multiple perspectives, including the connections between formal concepts and 3-valued concepts, and the meet-preserving mappings from formal concept lattices to 3-valued concept lattices. After that, based on the completions of 3-valued contexts, the connections between 3-valued concept lattices and three-way concept lattices are explored. Finally, it is proved that a 3-valued concept lattice is the minimum closure that contains formal concept lattices, and there is an order-preserving mapping from formal concepts to equivalence classes of 3-valued concepts.
{"title":"The properties of 3-valued formal contexts in a cognitive viewpoint","authors":"Huilai Zhi , Qing Wan , Ting Qian , Yinan Li , Jiang Yang","doi":"10.1016/j.ijar.2025.109573","DOIUrl":"10.1016/j.ijar.2025.109573","url":null,"abstract":"<div><div>3-valued formal contexts are abstracted from various types of applications such as incomplete formal context based data mining, shadow sets based knowledge discovery and conflict analysis. 3-valued formal contexts differ from binary-valued formal contexts in many aspects, and many distinguished details have not been investigated. To this end, some of the most important properties of 3-valued formal contexts are systematically explored in a cognitive viewpoint based on formal concept analysis. At first, 3-valued concept lattices and formal concept lattices are compared from multiple perspectives, including the connections between formal concepts and 3-valued concepts, and the meet-preserving mappings from formal concept lattices to 3-valued concept lattices. After that, based on the completions of 3-valued contexts, the connections between 3-valued concept lattices and three-way concept lattices are explored. Finally, it is proved that a 3-valued concept lattice is the minimum closure that contains formal concept lattices, and there is an order-preserving mapping from formal concepts to equivalence classes of 3-valued concepts.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109573"},"PeriodicalIF":3.0,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104298","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 : 2025-12-01Epub 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":"2025-12-01","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 : 2025-12-01Epub Date: 2025-07-17DOI: 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.
{"title":"Maximal consistent blocks-based optimistic and pessimistic probabilistic rough fuzzy sets and their applications in three-way multiple attribute decision-making","authors":"Yan Sun , Bin Pang , Ju-Sheng Mi , Wei-Zhi Wu","doi":"10.1016/j.ijar.2025.109529","DOIUrl":"10.1016/j.ijar.2025.109529","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"187 ","pages":"Article 109529"},"PeriodicalIF":3.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696895","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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