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Construction of interpretable hierarchical fuzzy systems subject to incomplete data 不完全数据下可解释层次模糊系统的构造
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-09 DOI: 10.1016/j.fss.2025.109273
Changle Sun , Haitao Li , Jun-e Feng
{"title":"Construction of interpretable hierarchical fuzzy systems subject to incomplete data","authors":"Changle Sun ,&nbsp;Haitao Li ,&nbsp;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}
引用次数: 0
Combinations of lattice-valued coarse structures and groups 格值粗结构与群的组合
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-08 DOI: 10.1016/j.fss.2025.109262
Yongchao Wang , Bin Pang , Fu-Gui Shi
{"title":"Combinations of lattice-valued coarse structures and groups","authors":"Yongchao Wang ,&nbsp;Bin Pang ,&nbsp;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}
引用次数: 0
Interval type-2 fuzzy H∞ filtering for nonlinear singularly perturbed jumping systems: A semi-Markov kernel method 非线性奇摄动跳跃系统的区间2型模糊H∞滤波：半马尔可夫核方法
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-08 DOI: 10.1016/j.fss.2025.109264
Hao Shen , Guanqi Wang , Jianwei Xia , Ju H. Park , Xiang-Peng Xie
{"title":"Interval type-2 fuzzy H∞ filtering for nonlinear singularly perturbed jumping systems: A semi-Markov kernel method","authors":"Hao Shen ,&nbsp;Guanqi Wang ,&nbsp;Jianwei Xia ,&nbsp;Ju H. Park ,&nbsp;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}
引用次数: 0
Prescribed-performance-based adaptive fuzzy asymptotic formation control for MIMO nonlinear multi-agent systems with infinite actuator faults 具有无限执行器故障的MIMO非线性多智能体系统的基于规定性能的自适应模糊渐近群控制
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-08 DOI: 10.1016/j.fss.2025.109263
Jun Zhang , Yi Zuo , Shaocheng Tong
{"title":"Prescribed-performance-based adaptive fuzzy asymptotic formation control for MIMO nonlinear multi-agent systems with infinite actuator faults","authors":"Jun Zhang ,&nbsp;Yi Zuo ,&nbsp;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}
引用次数: 0
Learning possibilistic dynamic systems from state transitions 从状态转换中学习可能性动态系统
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-06 DOI: 10.1016/j.fss.2024.109259
Hongbo Hu , Yisong Wang , Katsumi Inoue
{"title":"Learning possibilistic dynamic systems from state transitions","authors":"Hongbo Hu ,&nbsp;Yisong Wang ,&nbsp;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}
引用次数: 0
Stopping time estimation of first order multidimensional interval-valued differential equations 一阶多维区间值微分方程的停止时间估计
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-03 DOI: 10.1016/j.fss.2024.109260
Hongzhou Wang , Rosana Rodríguez-López
{"title":"Stopping time estimation of first order multidimensional interval-valued differential equations","authors":"Hongzhou Wang ,&nbsp;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}
引用次数: 0
The law of iterated expectation and imprecise probabilities 反复期望和不精确概率的法则
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-03 DOI: 10.1016/j.fss.2024.109258
Enrique Miranda , Arthur Van Camp
{"title":"The law of iterated expectation and imprecise probabilities","authors":"Enrique Miranda ,&nbsp;Arthur Van Camp","doi":"10.1016/j.fss.2024.109258","DOIUrl":"10.1016/j.fss.2024.109258","url":null,"abstract":"<div><div>The law of iterated expectation tells us how to combine hierarchical pieces of information when our uncertainty is modelled by means of probability measures. It has been extended to the imprecise case through Walley's marginal extension theorem for coherent lower previsions. In this paper, we investigate the extent to which a similar result can be established for other imprecise probability models that are either more general (choice functions) or more particular (possibility measures, belief functions) than coherent lower previsions. By doing this, we also establish links with other results established in the literature in the context of imprecise versions of Jeffrey's rule.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109258"},"PeriodicalIF":3.2,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical depth and support medians for fuzzy data 模糊数据的统计深度和支持中值
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-01-03 DOI: 10.1016/j.fss.2024.109257
Luis González-De La Fuente , Alicia Nieto-Reyes , Pedro Terán
{"title":"Statistical depth and support medians for fuzzy data","authors":"Luis González-De La Fuente ,&nbsp;Alicia Nieto-Reyes ,&nbsp;Pedro Terán","doi":"10.1016/j.fss.2024.109257","DOIUrl":"10.1016/j.fss.2024.109257","url":null,"abstract":"<div><div>Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-depth and projection depth.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109257"},"PeriodicalIF":3.2,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143158905","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}
引用次数: 0
Event-triggered-based fuzzy adaptive tracking control for stochastic nonlinear systems against multiple constraints 多约束随机非线性系统的事件触发模糊自适应跟踪控制
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-31 DOI: 10.1016/j.fss.2024.109253
Haina Zhao , Junsheng Zhao , Zong-Yao Sun , Dengxiu Yu
{"title":"Event-triggered-based fuzzy adaptive tracking control for stochastic nonlinear systems against multiple constraints","authors":"Haina Zhao ,&nbsp;Junsheng Zhao ,&nbsp;Zong-Yao Sun ,&nbsp;Dengxiu Yu","doi":"10.1016/j.fss.2024.109253","DOIUrl":"10.1016/j.fss.2024.109253","url":null,"abstract":"<div><div>In this article, we propose an adaptive event-triggered fuzzy dynamic surface controller for non-strict feedback stochastic nonlinear systems, where the nonlinear stochastic system exhibits input dead-zone characteristics and state constraints. Firstly, in contrast to many existing adaptive backstepping control results, we consider designing a dynamic surface control strategy to simplify complexity and enhance performance in stochastic systems. Then, the unknown nonlinearities within the system are addressed with the help of the approximation capability of the fuzzy logic system. It is worth noting that the design of the event-triggered mechanism effectively reduces resource waste in the data channel and improves communication efficiency. In addition, the adaptive backstepping control is combined with the barrier Lyapunov function in a unified framework to handle the state constraints. Resorting to a novel auxiliary system, the effect of the input dead-zone nonlinearity is countered. The presented fuzzy dynamic surface control scheme not only ensures the semi-globally uniformly ultimately bounded of the controlled system but also constrains the state within a fixed range and gets rid of the Zeno phenomenon. Finally, numerical simulation results validate the effectiveness of the control strategy and illustrate the feasibility of the controller through a single-link manipulator system.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109253"},"PeriodicalIF":3.2,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143158904","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}
引用次数: 0
Properties of fuzzy set spaces with Lp metrics 具有Lp度量的模糊集合空间的性质
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-12-31 DOI: 10.1016/j.fss.2024.109256
Huan Huang
{"title":"Properties of fuzzy set spaces with Lp metrics","authors":"Huan Huang","doi":"10.1016/j.fss.2024.109256","DOIUrl":"10.1016/j.fss.2024.109256","url":null,"abstract":"<div><div>This paper discusses the properties of the spaces of fuzzy sets in a metric space with <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-type <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics, <span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>. The <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics are well-defined if and only if the corresponding Haudorff distance functions are measurable. In this paper, we give several fundamental conclusions on the measurability of these Haudorff distance functions. Then we give some characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces with <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics. At last we present the completions of fuzzy set spaces with <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> metrics.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"504 ","pages":"Article 109256"},"PeriodicalIF":3.2,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143158903","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}
引用次数: 0
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