Pub Date : 2025-01-15DOI: 10.1016/j.fss.2025.109281
Chuang Zheng
In this paper, we extend the research presented in [26] by establishing the algebraic structure of the Gaussian Probability Density Membership Function (Gaussian-PDMF) space. We provide the explicit form of the membership function. Under the assumptions that all membership functions belongs to Gaussian-PDMF space, each fuzzy number can be uniquely identified by a vector. We introduce five operators: addition, subtraction, multiplication, scalar multiplication, and division. We demonstrate that, based on our definitions, the Gaussian-PDMF space exhibits a well-defined algebraic structure. For instance, it is a vector space over real numbers, featuring a subset that forms a division ring, allowing for the representation of fuzzy polynomials, among other properties. We provide several examples to illustrate our theoretical results.
{"title":"Algebraic structure of the Gaussian-PDMF space and applications on fuzzy equations","authors":"Chuang Zheng","doi":"10.1016/j.fss.2025.109281","DOIUrl":"10.1016/j.fss.2025.109281","url":null,"abstract":"<div><div>In this paper, we extend the research presented in <span><span>[26]</span></span> by establishing the algebraic structure of the Gaussian Probability Density Membership Function (Gaussian-PDMF) space. We provide the explicit form of the membership function. Under the assumptions that all membership functions belongs to Gaussian-PDMF space, each fuzzy number can be uniquely identified by a vector. We introduce five operators: addition, subtraction, multiplication, scalar multiplication, and division. We demonstrate that, based on our definitions, the Gaussian-PDMF space exhibits a well-defined algebraic structure. For instance, it is a vector space over real numbers, featuring a subset that forms a division ring, allowing for the representation of fuzzy polynomials, among other properties. We provide several examples to illustrate our theoretical results.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109281"},"PeriodicalIF":3.2,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181060","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 : 2025-01-10DOI: 10.1016/j.fss.2025.109276
Haitao Gan, Zhi Yang, Ming Shi, Zhiwei Ye, Ran Zhou
In recent years, the concept of safe semi-supervised clustering (S3C) has received increasing attention within the semi-supervised learning community. Generally, existing S3C methods first analyze the risk of labeled instances and then try to mitigate the corresponding negative impacts through various risk-based regularization approaches. However, the adverse effects of high-probability mislabeled instances (HPMIs) are not eliminated, and corresponding useful discriminative information is not discovered effectively. To address these issues, we propose an improved S3C method based on capped norm, called CapS3FCM. The motivation is that the capped norm can effectively filter or find mislabeled instances. Consequently, CapS3FCM introduces two capped norms. The first norm aims to make use of label information while simultaneously alleviating negative influences of mislabeled instances, especially HPMIs. The second norm further aims to discover useful discriminative information of those HPMIs. Finally, a loss function based on the capped norms is built, and the optimization problem is solved using an efficient iterative optimization strategy. To verify the effectiveness of CapS3FCM, a series of experiments is carried out on several datasets, which demonstrate that CapS3FCM can outperform the other semi-supervised and S3C methods. These findings validate that the capped norm is both practical and effective.
{"title":"Improved safe semi-supervised clustering based on capped ℓ21 norm","authors":"Haitao Gan, Zhi Yang, Ming Shi, Zhiwei Ye, Ran Zhou","doi":"10.1016/j.fss.2025.109276","DOIUrl":"10.1016/j.fss.2025.109276","url":null,"abstract":"<div><div>In recent years, the concept of safe semi-supervised clustering (S3C) has received increasing attention within the semi-supervised learning community. Generally, existing S3C methods first analyze the risk of labeled instances and then try to mitigate the corresponding negative impacts through various risk-based regularization approaches. However, the adverse effects of high-probability mislabeled instances (HPMIs) are not eliminated, and corresponding useful discriminative information is not discovered effectively. To address these issues, we propose an improved S3C method based on capped <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>21</mn></mrow></msub></math></span> norm, called CapS3FCM. The motivation is that the capped <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>21</mn></mrow></msub></math></span> norm can effectively filter or find mislabeled instances. Consequently, CapS3FCM introduces two capped <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>21</mn></mrow></msub></math></span> norms. The first norm aims to make use of label information while simultaneously alleviating negative influences of mislabeled instances, especially HPMIs. The second norm further aims to discover useful discriminative information of those HPMIs. Finally, a loss function based on the capped <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>21</mn></mrow></msub></math></span> norms is built, and the optimization problem is solved using an efficient iterative optimization strategy. To verify the effectiveness of CapS3FCM, a series of experiments is carried out on several datasets, which demonstrate that CapS3FCM can outperform the other semi-supervised and S3C methods. These findings validate that the capped <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>21</mn></mrow></msub></math></span> norm is both practical and effective.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109276"},"PeriodicalIF":3.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181061","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 : 2025-01-09DOI: 10.1016/j.fss.2024.109261
Changqing Li , Yanlan Zhang
In this note, we answer an open question, which is related to completion of principal fuzzy metric spaces in the sense of George and Veeramani, proposed by Gregori et al. (2012) [5]. We give a negative answer to such a question by means of an example.
在本论文中，我们将回答一个开放性问题，这个问题与 Gregori 等人（2012）[5] 提出的 George 和 Veeramani 意义上的主模糊度量空间的完备性有关。我们通过一个例子给出了对这个问题的否定回答。
{"title":"On completion of principal fuzzy metric spaces","authors":"Changqing Li , Yanlan Zhang","doi":"10.1016/j.fss.2024.109261","DOIUrl":"10.1016/j.fss.2024.109261","url":null,"abstract":"<div><div>In this note, we answer an open question, which is related to completion of principal fuzzy metric spaces in the sense of George and Veeramani, proposed by Gregori et al. (2012) <span><span>[5]</span></span>. We give a negative answer to such a question by means of an example.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109261"},"PeriodicalIF":3.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182380","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 : 2025-01-09DOI: 10.1016/j.fss.2025.109272
Yan Liu , Fang Liu , Qiang Shao
The higher-order Takagi-Sugeno-Kang (TSK) model, renowned for its interpretability, adaptability, robustness, and ease of training, has been extensively utilized in fuzzy inference and modeling. However, there has been a noticeable scarcity of studies exploring its counterparts in the complex-valued domain, particularly employing fully complex-valued mechanisms. Therefore, this paper introduced an adaptive fully complex-valued fuzzy inference system (AFCFIS). Leveraging Wirtinger calculus, the paper found partial derivatives and updated the network weights according to the gradient descent method, which was easily solved due to the fully complex-valued learning mechanism. Furthermore, the paper provided convergence results of the proposed algorithm under mild conditions. Finally, numerical simulations verified the convergence of AFCFIS, and demonstrated its good performance in both real and complex domain tasks, as well as both regression and classification tasks.
{"title":"Weak and strong convergence analysis of fully complex-valued high-order TSK model","authors":"Yan Liu , Fang Liu , Qiang Shao","doi":"10.1016/j.fss.2025.109272","DOIUrl":"10.1016/j.fss.2025.109272","url":null,"abstract":"<div><div>The higher-order Takagi-Sugeno-Kang (TSK) model, renowned for its interpretability, adaptability, robustness, and ease of training, has been extensively utilized in fuzzy inference and modeling. However, there has been a noticeable scarcity of studies exploring its counterparts in the complex-valued domain, particularly employing fully complex-valued mechanisms. Therefore, this paper introduced an adaptive fully complex-valued fuzzy inference system (AFCFIS). Leveraging Wirtinger calculus, the paper found partial derivatives and updated the network weights according to the gradient descent method, which was easily solved due to the fully complex-valued learning mechanism. Furthermore, the paper provided convergence results of the proposed algorithm under mild conditions. Finally, numerical simulations verified the convergence of AFCFIS, and demonstrated its good performance in both real and complex domain tasks, as well as both regression and classification tasks.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109272"},"PeriodicalIF":3.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181062","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 : 2025-01-09DOI: 10.1016/j.fss.2025.109273
Changle Sun , Haitao Li , Jun-e Feng
Hierarchical fuzzy systems (HFSs) are a significant branch of fuzzy systems. In this paper, the algebraic formulation of interpretable HFSs is investigated, and two algorithms are developed for the construction of interpretable HFSs subject to incomplete data. Firstly, the interpretable fuzzy logic unit (FLU) is presented and its algebraic formulation is developed by using the semi-tensor product of matrices. Secondly, by substituting the interpretable FLUs into the hierarchical structure, the interpretable HFSs are obtained. Thirdly, based on the proximal policy optimization, both direct and indirect algorithms are established to construct the interpretable HFSs subject to incomplete input-output data. Finally, the effectiveness of obtained results is verified by the on-ramp metering of freeway.
{"title":"Construction of interpretable hierarchical fuzzy systems subject to incomplete data","authors":"Changle Sun , Haitao Li , Jun-e Feng","doi":"10.1016/j.fss.2025.109273","DOIUrl":"10.1016/j.fss.2025.109273","url":null,"abstract":"<div><div>Hierarchical fuzzy systems (HFSs) are a significant branch of fuzzy systems. In this paper, the algebraic formulation of interpretable HFSs is investigated, and two algorithms are developed for the construction of interpretable HFSs subject to incomplete data. Firstly, the interpretable fuzzy logic unit (FLU) is presented and its algebraic formulation is developed by using the semi-tensor product of matrices. Secondly, by substituting the interpretable FLUs into the hierarchical structure, the interpretable HFSs are obtained. Thirdly, based on the proximal policy optimization, both direct and indirect algorithms are established to construct the interpretable HFSs subject to incomplete input-output data. Finally, the effectiveness of obtained results is verified by the on-ramp metering of freeway.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109273"},"PeriodicalIF":3.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182378","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 : 2025-01-08DOI: 10.1016/j.fss.2025.109262
Yongchao Wang , Bin Pang , Fu-Gui Shi
Based on a complete residuated lattice L, we combine the lattice-valued coarse structures and group operations to propose the concept of L-fuzzifying coarse groups. Then we introduce the notion of L-fuzzifying group ideals and establish its one-to-one correspondence with L-fuzzifying coarse groups. Specifically, we examine how L-fuzzifying coarse structures align with the algebraic structures of the supporting group. Finally, we use L-fuzzifying group ideals to characterize a fuzzy coarse equivalence between L-fuzzifying coarse groups, presenting some results derived from the kernel of the group homomorphism.
{"title":"Combinations of lattice-valued coarse structures and groups","authors":"Yongchao Wang , Bin Pang , Fu-Gui Shi","doi":"10.1016/j.fss.2025.109262","DOIUrl":"10.1016/j.fss.2025.109262","url":null,"abstract":"<div><div>Based on a complete residuated lattice <em>L</em>, we combine the lattice-valued coarse structures and group operations to propose the concept of <em>L</em>-fuzzifying coarse groups. Then we introduce the notion of <em>L</em>-fuzzifying group ideals and establish its one-to-one correspondence with <em>L</em>-fuzzifying coarse groups. Specifically, we examine how <em>L</em>-fuzzifying coarse structures align with the algebraic structures of the supporting group. Finally, we use <em>L</em>-fuzzifying group ideals to characterize a fuzzy coarse equivalence between <em>L</em>-fuzzifying coarse groups, presenting some results derived from the kernel of the group homomorphism.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109262"},"PeriodicalIF":3.2,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143181057","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 : 2025-01-08DOI: 10.1016/j.fss.2025.109264
Hao Shen , Guanqi Wang , Jianwei Xia , Ju H. Park , Xiang-Peng Xie
This paper addresses the filtering issue for nonlinear singularly perturbed jump systems with semi-Markov process. The interval type-2 fuzzy model is employed to handle the uncertain features and nonlinearity inherent in the considered systems. Designing an interval type-2 fuzzy filter, it is related to the system mode but remains independent of the singular perturbation parameter, this approach utilizes the semi-Markov kernel method and non-parallel distributed compensation technique. Some criteria with incorporating the message of membership functions are derived to ensure that the filtering error system is mean-square exponentially stable while meeting specified performance. Introduction of slack matrices with two adjustable scalars facilitates obtaining the interval type-2 fuzzy filter gains. The rationality of the proposed approach is demonstrated through the utilization of two examples, including a circuit model.
{"title":"Interval type-2 fuzzy H∞ filtering for nonlinear singularly perturbed jumping systems: A semi-Markov kernel method","authors":"Hao Shen , Guanqi Wang , Jianwei Xia , Ju H. Park , Xiang-Peng Xie","doi":"10.1016/j.fss.2025.109264","DOIUrl":"10.1016/j.fss.2025.109264","url":null,"abstract":"<div><div>This paper addresses the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> filtering issue for nonlinear singularly perturbed jump systems with semi-Markov process. The interval type-2 fuzzy model is employed to handle the uncertain features and nonlinearity inherent in the considered systems. Designing an interval type-2 fuzzy filter, it is related to the system mode but remains independent of the singular perturbation parameter, this approach utilizes the semi-Markov kernel method and non-parallel distributed compensation technique. Some criteria with incorporating the message of membership functions are derived to ensure that the filtering error system is mean-square exponentially stable while meeting specified <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> performance. Introduction of slack matrices with two adjustable scalars facilitates obtaining the interval type-2 fuzzy filter gains. The rationality of the proposed approach is demonstrated through the utilization of two examples, including a circuit model.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109264"},"PeriodicalIF":3.2,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182377","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 : 2025-01-08DOI: 10.1016/j.fss.2025.109263
Jun Zhang , Yi Zuo , Shaocheng Tong
In this article, the adaptive fuzzy asymptotic formation fault-tolerant control (FTC) problem is investigated for multi-input and multi-output (MIMO) nonlinear multi-agent systems (MASs) with infinite actuator faults. The controlled plant contains unknown nonlinear dynamics and infinite actuator faults. The unknown nonlinear dynamics are handled by using fuzzy approximation technique. The virtual controllers together with the parameter adaptive laws are obtained by introducing an integrable function and utilizing bounded estimation algorithms. To overcome the difficulty caused by the infinite actuator faults, a novel actuator fault compensation method is presented based on a two-step design technique. By introducing a prescribed performance function (PPF) to the backstepping recursive design, an adaptive fuzzy asymptotic formation FTC scheme is developed. Based on the Lyapunov stability theory, it is proved that the closed-loop signals are all bounded, the formation error converges asymptotically to zero, and the convergence rate and maximum overshoot of the formation error can be guaranteed. Finally, the developed formation FTC is applied to a group of marine surface vehicles, and its effectiveness and practicability are verified.
{"title":"Prescribed-performance-based adaptive fuzzy asymptotic formation control for MIMO nonlinear multi-agent systems with infinite actuator faults","authors":"Jun Zhang , Yi Zuo , Shaocheng Tong","doi":"10.1016/j.fss.2025.109263","DOIUrl":"10.1016/j.fss.2025.109263","url":null,"abstract":"<div><div>In this article, the adaptive fuzzy asymptotic formation fault-tolerant control (FTC) problem is investigated for multi-input and multi-output (MIMO) nonlinear multi-agent systems (MASs) with infinite actuator faults. The controlled plant contains unknown nonlinear dynamics and infinite actuator faults. The unknown nonlinear dynamics are handled by using fuzzy approximation technique. The virtual controllers together with the parameter adaptive laws are obtained by introducing an integrable function and utilizing bounded estimation algorithms. To overcome the difficulty caused by the infinite actuator faults, a novel actuator fault compensation method is presented based on a two-step design technique. By introducing a prescribed performance function (PPF) to the backstepping recursive design, an adaptive fuzzy asymptotic formation FTC scheme is developed. Based on the Lyapunov stability theory, it is proved that the closed-loop signals are all bounded, the formation error converges asymptotically to zero, and the convergence rate and maximum overshoot of the formation error can be guaranteed. Finally, the developed formation FTC is applied to a group of marine surface vehicles, and its effectiveness and practicability are verified.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109263"},"PeriodicalIF":3.2,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182381","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 : 2025-01-06DOI: 10.1016/j.fss.2024.109259
Hongbo Hu , Yisong Wang , Katsumi Inoue
Learning from 1-step transitions (LF1T) has become a paradigm to construct a logical hypothesis of a dynamic system, such as a Boolean network, from its synchronized state transitions and background knowledge. While uncertain and incomplete information plays an important role in dynamic systems, LF1T and its successors cannot handle uncertainty modeled by possibility theory. This motivates our combination of inductive logic programming (ILP) and possibilistic normal logic program (poss-NLP) that applies to reasoning about uncertain dynamic systems. In this paper, we propose a learning task to learn a poss-NLP from given interpretation transitions and background knowledge. The sufficient and necessary condition for the existence of its solution is determined. We introduce an algorithm called iltp to learn a specific solution, which typically encompasses mass redundant rules. Additionally, we propose another algorithm called sp-iltp to identify global minimal solutions. Alongside theoretical correctness proofs, a synthetic experiment demonstrates the learning performance on six gene regulatory networks with possibilistic uncertainty. This work thus offers a rational framework for learning the dynamics of systems under uncertainty via poss-NLPs.
{"title":"Learning possibilistic dynamic systems from state transitions","authors":"Hongbo Hu , Yisong Wang , Katsumi Inoue","doi":"10.1016/j.fss.2024.109259","DOIUrl":"10.1016/j.fss.2024.109259","url":null,"abstract":"<div><div>Learning from 1-step transitions (LF1T) has become a paradigm to construct a logical hypothesis of a dynamic system, such as a Boolean network, from its synchronized state transitions and background knowledge. While uncertain and incomplete information plays an important role in dynamic systems, LF1T and its successors cannot handle uncertainty modeled by possibility theory. This motivates our combination of inductive logic programming (ILP) and possibilistic normal logic program (poss-NLP) that applies to reasoning about uncertain dynamic systems. In this paper, we propose a learning task to learn a poss-NLP from given interpretation transitions and background knowledge. The sufficient and necessary condition for the existence of its solution is determined. We introduce an algorithm called <span>iltp</span> to learn a specific solution, which typically encompasses mass redundant rules. Additionally, we propose another algorithm called <span>sp-iltp</span> to identify global minimal solutions. Alongside theoretical correctness proofs, a synthetic experiment demonstrates the learning performance on six gene regulatory networks with possibilistic uncertainty. This work thus offers a rational framework for learning the dynamics of systems under uncertainty via poss-NLPs.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109259"},"PeriodicalIF":3.2,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143158906","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 : 2025-01-03DOI: 10.1016/j.fss.2024.109260
Hongzhou Wang , Rosana Rodríguez-López
Stopping time problem of first order multidimensional interval-valued dynamic system is discussed. By calculating stopping times of corresponding linear differential equations, we provide some estimation results of stopping times of forward and backward solutions to nonlinear interval-valued differential equations with respect to length or volume constraints. Then, stopping times of some linear and nonlinear interval-valued differential equations models, including predator-prey system, two species mutualism and competition systems, Lorenz equations, are studied as applications.
{"title":"Stopping time estimation of first order multidimensional interval-valued differential equations","authors":"Hongzhou Wang , Rosana Rodríguez-López","doi":"10.1016/j.fss.2024.109260","DOIUrl":"10.1016/j.fss.2024.109260","url":null,"abstract":"<div><div>Stopping time problem of first order multidimensional interval-valued dynamic system is discussed. By calculating stopping times of corresponding linear differential equations, we provide some estimation results of stopping times of forward and backward solutions to nonlinear interval-valued differential equations with respect to length or volume constraints. Then, stopping times of some linear and nonlinear interval-valued differential equations models, including predator-prey system, two species mutualism and competition systems, Lorenz equations, are studied as applications.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"505 ","pages":"Article 109260"},"PeriodicalIF":3.2,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143182379","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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