Pub Date : 2026-06-01Epub Date: 2026-01-14DOI: 10.1016/j.fss.2026.109774
M. Svistula, T. Sribnaya, R. Uzbekov
In the present paper we propose such an abstract setting, which allows us to obtain as consequences both known and new results on the coincidence of the Choquet integral and the pan-integral. For example: in the case of a measurable space we derive a well-known theorem that the weak (M)-property of a monotone measure is necessary and sufficient for the coincidence of the integrals under consideration for all nonnegative measurable integrands; in the case of a topological space we use the integrals with respect to a regular monotone measure and establish some new results, in particular, that the Choquet integral and the pan-integral with respect to a topological measure coincide for all nonnegative lower semicontinuous integrands.
Next, in the case of a measurable space we give an example to show that the weak (M)-property is weaker than the middle (M)-property, and thus we solve an open problem of the relationship between these properties.
{"title":"On the coincidence of the Choquet integral and the pan-integral: An abstract setting and examples","authors":"M. Svistula, T. Sribnaya, R. Uzbekov","doi":"10.1016/j.fss.2026.109774","DOIUrl":"10.1016/j.fss.2026.109774","url":null,"abstract":"<div><div>In the present paper we propose such an abstract setting, which allows us to obtain as consequences both known and new results on the coincidence of the Choquet integral and the pan-integral. For example: in the case of a measurable space we derive a well-known theorem that the weak (M)-property of a monotone measure is necessary and sufficient for the coincidence of the integrals under consideration for all nonnegative measurable integrands; in the case of a topological space we use the integrals with respect to a regular monotone measure and establish some new results, in particular, that the Choquet integral and the pan-integral with respect to a topological measure coincide for all nonnegative lower semicontinuous integrands.</div><div>Next, in the case of a measurable space we give an example to show that the weak (M)-property is weaker than the middle (M)-property, and thus we solve an open problem of the relationship between these properties.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109774"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-28DOI: 10.1016/j.fss.2026.109800
J. Graña-Colubi , G. González-Rodríguez , A.B. Ramos-Guajardo
The estimation of a simple linear regression model is undertaken when both the independent and dependent variables are star-shaped set-valued random elements. The suggested regression model is defined by using the set arithmetic, assuming that the components representing location and imprecision of the random elements in the model are handled independently. Once the theoretical framework is established, the least squares estimation for the linear model is performed, taking into account an appropriate distance within the space of star-shaped sets. This approach results in a constrained minimization problem, which is analytically solved. Furthermore, the strong consistency of the obtained estimators is analyzed. Finally, the model is applied to a real-life situation and a simulation study is carried out.
{"title":"Estimation of a simple linear regression model for random star-shaped sets","authors":"J. Graña-Colubi , G. González-Rodríguez , A.B. Ramos-Guajardo","doi":"10.1016/j.fss.2026.109800","DOIUrl":"10.1016/j.fss.2026.109800","url":null,"abstract":"<div><div>The estimation of a simple linear regression model is undertaken when both the independent and dependent variables are star-shaped set-valued random elements. The suggested regression model is defined by using the set arithmetic, assuming that the components representing location and imprecision of the random elements in the model are handled independently. Once the theoretical framework is established, the least squares estimation for the linear model is performed, taking into account an appropriate distance within the space of star-shaped sets. This approach results in a constrained minimization problem, which is analytically solved. Furthermore, the strong consistency of the obtained estimators is analyzed. Finally, the model is applied to a real-life situation and a simulation study is carried out.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109800"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-22DOI: 10.1016/j.fss.2026.109794
Paulo Vitor de Campos Souza
This study presents the pseudo-FNN, a fuzzy neural network model that integrates the pseudo-unineuron, a novel neuron type leveraging pseudo-uninorms to enhance non-commutative operations and knowledge extraction. The pseudo-FNN employs a three-layer architecture with Gaussian fuzzy neurons, where weights are derived from kernel density estimation and rule consequents are optimized using multiple algorithms. Experimental evaluations on four datasets (Iris, Haberman, Transfusion, and Mammographic Masses) demonstrate the model’s competitive performance. The pseudo-FNN outperformed traditional fuzzy neural networks such as ANFIS and showed comparable results with optimization-enhanced FNNs. Among the optimization techniques, models using SGD, Adam, and RMSProp achieved the most consistent and high accuracies across datasets with pseudo-FNN models often aligning with these trends. Statistical analysis confirmed significant improvements over non-optimized models, and the pseudo-FNN demonstrated robustness in addressing varying classification complexities. These results highlight the effectiveness of the pseudo-unineuron in advancing fuzzy neural network architectures.
{"title":"pseudo-FNN: Advancing fuzzy neural networks with pseudo-Unineurons and kernel density-based weights","authors":"Paulo Vitor de Campos Souza","doi":"10.1016/j.fss.2026.109794","DOIUrl":"10.1016/j.fss.2026.109794","url":null,"abstract":"<div><div>This study presents the pseudo-FNN, a fuzzy neural network model that integrates the pseudo-unineuron, a novel neuron type leveraging pseudo-uninorms to enhance non-commutative operations and knowledge extraction. The pseudo-FNN employs a three-layer architecture with Gaussian fuzzy neurons, where weights are derived from kernel density estimation and rule consequents are optimized using multiple algorithms. Experimental evaluations on four datasets (Iris, Haberman, Transfusion, and Mammographic Masses) demonstrate the model’s competitive performance. The pseudo-FNN outperformed traditional fuzzy neural networks such as ANFIS and showed comparable results with optimization-enhanced FNNs. Among the optimization techniques, models using SGD, Adam, and RMSProp achieved the most consistent and high accuracies across datasets with pseudo-FNN models often aligning with these trends. Statistical analysis confirmed significant improvements over non-optimized models, and the pseudo-FNN demonstrated robustness in addressing varying classification complexities. These results highlight the effectiveness of the pseudo-unineuron in advancing fuzzy neural network architectures.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109794"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-24DOI: 10.1016/j.fss.2026.109798
Xia Jiang, Kaichao Zhang, Xuan Zhao
To improve the computational efficiency of failure possibility estimation in fuzzy reliability analysis, this paper proposes an Adaptive Directional Importance Sampling method (ADIS), which employs a von Mises–Fisher mixture (vMFM) model as the sampling density of direction vectors. The initial vMFM parameters are determined through uniform pre-sampling and clustering of failure samples by using the density-based spatial clustering of applications with noise clustering (DBSCAN) algorithm, while an intermediate event is introduced to address the scarcity of failure samples. During the adaptive iterative process, direction vectors are continuously drawn from the updated vMFM model, and their intersection points with the limit-state surface are obtained using an iterative root-finding strategy. Based on these intersection points, the vMFM parameters are iteratively refined through DBSCAN clustering and the expectation-maximization (EM) algorithm. Iteration continues until the updated vMFM model generates a sufficient number of direction vectors pointing to the true failure domain, yielding a quasi-optimal sampling density. Finally, the failure possibility is efficiently estimated by all accumulated intersection points throughout the iterative process. Example analyses demonstrate that the proposed method achieves superior efficiency compared with traditional directional simulation and existing simulation strategies.
{"title":"Adaptive directional importance sampling with von Mises-Fisher mixture model for fuzzy reliability analysis","authors":"Xia Jiang, Kaichao Zhang, Xuan Zhao","doi":"10.1016/j.fss.2026.109798","DOIUrl":"10.1016/j.fss.2026.109798","url":null,"abstract":"<div><div>To improve the computational efficiency of failure possibility estimation in fuzzy reliability analysis, this paper proposes an <strong>A</strong>daptive <strong>D</strong>irectional <strong>I</strong>mportance <strong>S</strong>ampling method (ADIS), which employs a von Mises–Fisher mixture (vMFM) model as the sampling density of direction vectors. The initial vMFM parameters are determined through uniform pre-sampling and clustering of failure samples by using the density-based spatial clustering of applications with noise clustering (DBSCAN) algorithm, while an intermediate event is introduced to address the scarcity of failure samples. During the adaptive iterative process, direction vectors are continuously drawn from the updated vMFM model, and their intersection points with the limit-state surface are obtained using an iterative root-finding strategy. Based on these intersection points, the vMFM parameters are iteratively refined through DBSCAN clustering and the expectation-maximization (EM) algorithm. Iteration continues until the updated vMFM model generates a sufficient number of direction vectors pointing to the true failure domain, yielding a quasi-optimal sampling density. Finally, the failure possibility is efficiently estimated by all accumulated intersection points throughout the iterative process. Example analyses demonstrate that the proposed method achieves superior efficiency compared with traditional directional simulation and existing simulation strategies.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109798"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-20DOI: 10.1016/j.fss.2026.109791
Taras Banakh , Krzysztof Caban , Filip Strobin
In the paper we unify two extensions of the classical Hutchinson–Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuzzy IFS) on a Tychonoff space X which is contracting w.r.t. some admissible multimetric, generates a natural fuzzy attractor in the hyperspace of all compact fuzzy sets. As a consequence, we prove that a fuzzy IFS on a Hausdorff topological space which is topologically contracting admits a fuzzy attractor in a bit weaker sense. Our discussion involves investigations on topologies on the hyperspace which are suitable for establishing convergence of sequences of iterations of a fuzzy Hutchinson operator.
{"title":"A topological approach to fuzzy iterated function systems","authors":"Taras Banakh , Krzysztof Caban , Filip Strobin","doi":"10.1016/j.fss.2026.109791","DOIUrl":"10.1016/j.fss.2026.109791","url":null,"abstract":"<div><div>In the paper we unify two extensions of the classical Hutchinson–Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuzzy IFS) on a Tychonoff space <em>X</em> which is contracting w.r.t. some admissible multimetric, generates a natural fuzzy attractor in the hyperspace <span><math><mrow><msub><mi>K</mi><mi>F</mi></msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> of all compact fuzzy sets. As a consequence, we prove that a fuzzy IFS on a Hausdorff topological space which is topologically contracting admits a fuzzy attractor in a bit weaker sense. Our discussion involves investigations on topologies on the hyperspace <span><math><mrow><msub><mi>K</mi><mi>F</mi></msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> which are suitable for establishing convergence of sequences of iterations of a fuzzy Hutchinson operator.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109791"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-13DOI: 10.1016/j.fss.2026.109775
James C. Bezdek, Thomas A. Runkler
Possibilistic c-means (PCM) clustering began in 1993, and has been used since then in many applications. In this article we discuss the geometric foundations of PCM and introduce a new hard possibilistic c-means (HPCM) clustering algorithm. We use limit theory to prove that the extended set of possibilistic c-partitions is the unit hypercube in; and that its vertices are exactly the hard possibilistic c-partitions on n objects defined herein. This enables completion of the geometric description of the domain of possibilistic clustering algorithms. We give examples that compare the results of clustering with Hard c-means (HCM) to HPCM on three small synthetic data sets. Our proof-of-concept examples show that the new algorithm performs as expected, and provides much more realistic interpretation of clusters than HCM when the data contain bridge points or noise.
{"title":"Geometric foundations of possibilistic clustering: A hard possibilistic clustering algorithm","authors":"James C. Bezdek, Thomas A. Runkler","doi":"10.1016/j.fss.2026.109775","DOIUrl":"10.1016/j.fss.2026.109775","url":null,"abstract":"<div><div><em>Possibilistic c-means</em> (PCM) clustering began in 1993, and has been used since then in many applications. In this article we discuss the geometric foundations of PCM and introduce a new <em>hard possibilistic c-means</em> (HPCM) clustering algorithm. We use limit theory to prove that the extended set of possibilistic c-partitions is the unit hypercube in<span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>c</mi><mi>n</mi></mrow></msup></math></span>; and that its vertices are exactly the hard possibilistic c-partitions on n objects defined herein. This enables completion of the geometric description of the domain of possibilistic clustering algorithms. We give examples that compare the results of clustering with <em>Hard c-means</em> (HCM) to HPCM on three small synthetic data sets. Our proof-of-concept examples show that the new algorithm performs as expected, and provides much more realistic interpretation of clusters than HCM when the data contain bridge points or noise.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109775"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-22DOI: 10.1016/j.fss.2026.109790
Jaime Cesar dos Santos
Building upon specific compatibility conditions, we establish fundamental structural results concerning ordering relations for triangular fuzzy numbers. We demonstrate that orders satisfying compatibility with arithmetic operations, MIN-MAX operators, and the Weak Law of Trichotomy (WLT) are completely determined on the fibers of the natural projection to real numbers. Furthermore, such orders naturally induce — in analogy with real numbers — well-defined notions of fuzzy absolute value and fuzzy distance that preserve the essential properties of their classical counterparts. These results enable us to characterize open and closed balls through interval representations, providing a robust theoretical framework for future studies regarding metric properties of fuzzy numbers.
{"title":"Regular orders for triangular fuzzy numbers and the weak law of trichotomy","authors":"Jaime Cesar dos Santos","doi":"10.1016/j.fss.2026.109790","DOIUrl":"10.1016/j.fss.2026.109790","url":null,"abstract":"<div><div>Building upon specific compatibility conditions, we establish fundamental structural results concerning ordering relations for triangular fuzzy numbers. We demonstrate that orders satisfying compatibility with arithmetic operations, <em>MIN-MAX</em> operators, and the Weak Law of Trichotomy (WLT) are completely determined on the fibers of the natural projection to real numbers. Furthermore, such orders naturally induce — in analogy with real numbers — well-defined notions of fuzzy absolute value and fuzzy distance that preserve the essential properties of their classical counterparts. These results enable us to characterize open and closed balls through interval representations, providing a robust theoretical framework for future studies regarding metric properties of fuzzy numbers.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109790"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-23DOI: 10.1016/j.fss.2026.109795
Lu Wang , Yaya Liu , Keyun Qin , Zheng Pei
In granular computing, extracting effective features from imbalanced high-dimensional data remains a frontier challenge. Existing models for interval-valued fuzzy decision information systems (IFDS) have two critical limitations: fixed neighborhood radii fail to adapt to the local distribution characteristics of different features, and boundary information in granular structures is underutilized, leading to incomplete feature importance evaluation. For these limitations, we present a feature selection method for IFDS based on the double fuzzy adaptive neighborhood consistency measure. First, we define a novel fuzzy adaptive neighborhood radius to dynamically optimize the neighborhood structure, establish a fuzzy adaptive neighborhood rough set model for IFDS with rigorous axiomatic analysis, and further construct the double fuzzy adaptive neighborhood consistency measure to comprehensively capture deterministic and uncertain relationships between features and fuzzy decisions. Additionally, a matrix-based feature selection algorithm is designed to enhance computational efficiency for high-dimensional data. Through comparative experiments conducted on nine datasets, the experimental results demonstrate that the proposed model and algorithm achieve significant advantages in approximation accuracy and classification performance.
{"title":"Matrix -driven feature selection for interval-valued data based on double fuzzy adaptive neighborhood consistency measure","authors":"Lu Wang , Yaya Liu , Keyun Qin , Zheng Pei","doi":"10.1016/j.fss.2026.109795","DOIUrl":"10.1016/j.fss.2026.109795","url":null,"abstract":"<div><div>In granular computing, extracting effective features from imbalanced high-dimensional data remains a frontier challenge. Existing models for interval-valued fuzzy decision information systems (IFDS) have two critical limitations: fixed neighborhood radii fail to adapt to the local distribution characteristics of different features, and boundary information in granular structures is underutilized, leading to incomplete feature importance evaluation. For these limitations, we present a feature selection method for IFDS based on the double fuzzy adaptive neighborhood consistency measure. First, we define a novel fuzzy adaptive neighborhood radius to dynamically optimize the neighborhood structure, establish a fuzzy adaptive neighborhood rough set model for IFDS with rigorous axiomatic analysis, and further construct the double fuzzy adaptive neighborhood consistency measure to comprehensively capture deterministic and uncertain relationships between features and fuzzy decisions. Additionally, a matrix-based feature selection algorithm is designed to enhance computational efficiency for high-dimensional data. Through comparative experiments conducted on nine datasets, the experimental results demonstrate that the proposed model and algorithm achieve significant advantages in approximation accuracy and classification performance.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"532 ","pages":"Article 109795"},"PeriodicalIF":2.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we introduce the concept of Ω-vector spaces, extending the framework of Ω-algebras by incorporating a vector space structure over a field. These structures are defined over a complete lattice and equipped with an Ω-valued equality, which replaces the classical relation of being equal. We provide an equivalent characterization of Ω-vector spaces via cut-quotient structures and prove that each cut induces a classical vector space. Furthermore, we introduce the notion of Ω-vector subspaces and investigate the lattice-theoretic properties of their collection, including intersections and sums. Finally, we show an application for approximately solving systems of linear equations in this context. Several examples illustrate the theory, highlighting the algebraic richness and structural consistency of Ω-vector spaces.
{"title":"Ω-vector spaces","authors":"Patricia Ferrero , Jorge Jiménez , María Luisa Serrano , Branimir Šešelja , Andreja Tepavčević","doi":"10.1016/j.fss.2026.109776","DOIUrl":"10.1016/j.fss.2026.109776","url":null,"abstract":"<div><div>In this work, we introduce the concept of Ω-vector spaces, extending the framework of Ω-algebras by incorporating a vector space structure over a field. These structures are defined over a complete lattice and equipped with an Ω-valued equality, which replaces the classical relation of being equal. We provide an equivalent characterization of Ω-vector spaces via cut-quotient structures and prove that each cut induces a classical vector space. Furthermore, we introduce the notion of Ω-vector subspaces and investigate the lattice-theoretic properties of their collection, including intersections and sums. Finally, we show an application for approximately solving systems of linear equations in this context. Several examples illustrate the theory, highlighting the algebraic richness and structural consistency of Ω-vector spaces.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"531 ","pages":"Article 109776"},"PeriodicalIF":2.7,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-15Epub Date: 2026-01-20DOI: 10.1016/j.fss.2026.109789
Dong Qiu , Nianxi Huang , Yandan Jiang
In this paper, by using the properties of their endpoint-valued functions, we gave characterizations of various generalized differentiabilities of interval-valued functions and fuzzy number-valued functions, which provide more convenient calculating and discriminating formulas than directly according to the definitions. By comparing these characterizations, we revealed the complete and detailed connection between the different types of differentiabilities. In addition, for n-fold interval-valued functions, we proposed two new definitions: combined gH-differentiability of coordinate components and metric-based differentiability in coordinates, to generalize existing differentiabilities; for fuzzy number-valued functions, we introduced gH⁎⁎-differentiability to improve the existing gH*-differentiability. The obtained results extend and improve the ones in the literature.
{"title":"Characterizations and relation of generalized differentiabilities of interval-valued functions and fuzzy number-valued functions","authors":"Dong Qiu , Nianxi Huang , Yandan Jiang","doi":"10.1016/j.fss.2026.109789","DOIUrl":"10.1016/j.fss.2026.109789","url":null,"abstract":"<div><div>In this paper, by using the properties of their endpoint-valued functions, we gave characterizations of various generalized differentiabilities of interval-valued functions and fuzzy number-valued functions, which provide more convenient calculating and discriminating formulas than directly according to the definitions. By comparing these characterizations, we revealed the complete and detailed connection between the different types of differentiabilities. In addition, for <em>n</em>-fold interval-valued functions, we proposed two new definitions: combined <em>gH</em>-differentiability of coordinate components and metric-based differentiability in coordinates, to generalize existing differentiabilities; for fuzzy number-valued functions, we introduced <em>gH</em><sup>⁎⁎</sup>-differentiability to improve the existing <em>gH</em>*-differentiability. The obtained results extend and improve the ones in the literature.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"531 ","pages":"Article 109789"},"PeriodicalIF":2.7,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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