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On monotone measures that provide the coincidence of the Choquet integral and the pan-integral 提供Choquet积分与泛积分重合的单调测度
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-06-06 DOI: 10.1016/j.fss.2025.109501
M. Svistula
{"title":"On monotone measures that provide the coincidence of the Choquet integral and the pan-integral","authors":"M. Svistula","doi":"10.1016/j.fss.2025.109501","DOIUrl":"10.1016/j.fss.2025.109501","url":null,"abstract":"<div><div>It is known that the (M)-property and the weak (M)-property of monotone measures were introduced in the studying the coincidence of the Choquet integral and the pan-integral. We proved that for a finite monotone measure, which is continuous from above, these two properties are equivalent. Besides that, some new properties and a criterion for additivity of monotone measures with the (M)-property and the weak (M)-property were presented. We also introduce the notion of the middle (M)-property and rise an open problem with the relationship between this property and the weak (M)-property.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109501"},"PeriodicalIF":3.2,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241818","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
Memory-based attack-tolerant T-S fuzzy control of networked artificial pancreas system subject to false data injection attacks 虚假数据注入攻击下网络化人工胰腺系统的记忆容错T-S模糊控制
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-06-04 DOI: 10.1016/j.fss.2025.109486
Shen Yan , Liming Ding , Yue Cai
{"title":"Memory-based attack-tolerant T-S fuzzy control of networked artificial pancreas system subject to false data injection attacks","authors":"Shen Yan ,&nbsp;Liming Ding ,&nbsp;Yue Cai","doi":"10.1016/j.fss.2025.109486","DOIUrl":"10.1016/j.fss.2025.109486","url":null,"abstract":"<div><div>This paper studies the memory-based attack-tolerant control issue of networked artificial pancreas system subject to false data injection attacks. First, a T-S fuzzy modeling approach and a T-S fuzzy observer based on sampled outputs are utilized to deal with the system nonlinearity and estimate full system state, respectively. Second, to maintain the system security in the presence of malicious attacks in the communication network, a radial basis function neural network-based estimator is introduced to approximate the real attack signal. Then, with the utilization of estimated state, memory state related to sampled period and approximated attack, a memory-based attack-tolerant T-S fuzzy controller is constructed to restore the blood glucose levels within a safe range. Third, some novel sufficient conditions formed in a set of linear matrix inequalities are derived to solve the controller and observer gains. Finally, the advantages of the proposed blood glucose regulation scheme are confirmed through illustrative simulation outcomes.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109486"},"PeriodicalIF":3.2,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230148","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
A fuzzy set-based methodology for autonomous navigation 基于模糊集的自主导航方法
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-06-03 DOI: 10.1016/j.fss.2025.109485
Ehsan Adel Rastkhiz, Howard Schwartz, Ioannis Lambadaris
{"title":"A fuzzy set-based methodology for autonomous navigation","authors":"Ehsan Adel Rastkhiz,&nbsp;Howard Schwartz,&nbsp;Ioannis Lambadaris","doi":"10.1016/j.fss.2025.109485","DOIUrl":"10.1016/j.fss.2025.109485","url":null,"abstract":"<div><div>This paper presents a fuzzy set-based methodology to achieve simultaneous path adherence and local collision avoidance in autonomous navigation. It targets scenarios where a global path to the vehicle's destination is already planned but with imperfect knowledge of the obstacles in the environment and their dynamics. Assuming that the vehicle can localize itself and the obstacles around it, the proposed methodology incorporates the global path and the acquired real-time knowledge of the local obstacles by the vehicle to create a comprehensive fuzzy representation of the environment. This fuzzy representation is then utilized to assess the desirability of the vehicle states within an optimization framework that balances global path adherence and obstacle avoidance objectives. The proposed gradient-based solution to this optimization problem navigates the vehicle such that it maintains its global course toward the designated destination while avoiding collision with local obstacles. Extensive simulations on a mobile robot validate the method's efficacy in guiding vehicles along desired paths, maneuvering around obstacles with minimal deviation from the route, and negotiating local minima without oscillations. Additionally, simulation results highlight the proposed fuzzy set-based methodology's low computational complexity, real-time operation capability, and adaptability in handling complex geometries of paths and obstacles.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109485"},"PeriodicalIF":3.2,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230048","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
Fuzzy Green's relations and its applications in E-fuzzy semigroups 模糊格林关系及其在e -模糊半群中的应用
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-06-03 DOI: 10.1016/j.fss.2025.109482
Yuan Zhi , Qingguo Li , Xiangnan Zhou
{"title":"Fuzzy Green's relations and its applications in E-fuzzy semigroups","authors":"Yuan Zhi ,&nbsp;Qingguo Li ,&nbsp;Xiangnan Zhou","doi":"10.1016/j.fss.2025.109482","DOIUrl":"10.1016/j.fss.2025.109482","url":null,"abstract":"<div><div>Within the framework of fuzzy algebras with fuzzy equality and a complete lattice for membership values, this paper introduces a novel fuzzified version of classical Green's relations on <em>E</em>-fuzzy semigroups, referred to as <em>E</em>-fuzzy Green's relations. We reveal several properties of <em>E</em>-fuzzy semigroups, including the properties of fuzzy unit elements within <em>E</em>-fuzzy cancellative semigroups. Additionally, we derive equivalent forms of these newly defined fuzzy relations and examine the properties of their associated cut-quotient structures in certain <em>E</em>-fuzzy semigroups. The <em>E</em>-fuzzy Green's relations on <em>E</em>-fuzzy semigroups are found to be compatible fuzzy equivalence relations (fuzzy equalities) on some <em>E</em>-fuzzy bands. Furthermore, we present two significant decomposition theorems related to the cut-quotient structures over fuzzy Green's relations, demonstrating that these structures have additional algebraic properties compared with the quotient structures over ordinary fuzzy equality <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>μ</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109482"},"PeriodicalIF":3.2,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204998","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
A fractional spectral Galerkin method for fuzzy Volterra integral equations with weakly singular kernels: Regularity, convergence, and applications 弱奇异核模糊Volterra积分方程的分数阶谱伽辽金方法：正则性、收敛性和应用
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-06-03 DOI: 10.1016/j.fss.2025.109488
Younes Talaei , Mahmoud A. Zaky , Ahmed S. Hendy
{"title":"A fractional spectral Galerkin method for fuzzy Volterra integral equations with weakly singular kernels: Regularity, convergence, and applications","authors":"Younes Talaei ,&nbsp;Mahmoud A. Zaky ,&nbsp;Ahmed S. Hendy","doi":"10.1016/j.fss.2025.109488","DOIUrl":"10.1016/j.fss.2025.109488","url":null,"abstract":"<div><div>Fuzzy Volterra integral equations with weakly singular kernels have solutions with singular behavior at the origin. Utilizing spectral methods on such problems with standard (integer-order) basis functions leads to generating approximate solutions with low-order accuracy. This paper deals with improving the accuracy of the spectral Galerkin method which can be applied to such problems by using fractional-order basis functions. New matrix formulation of the proposed method transforms the problem under consideration into a system of algebraic equations with a simple structure. Numerical implementation of the constructed method shows its effectiveness compared to other methods. The convergence analysis of the method is theoretically investigated in a weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109488"},"PeriodicalIF":3.2,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241814","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
Updating information based on generalized credal sets. Part 3: Applications to statistical inference 基于广义凭证集的信息更新。第3部分：统计推断的应用
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-06-02 DOI: 10.1016/j.fss.2025.109483
Andrey G. Bronevich , Igor N. Rozenberg
{"title":"Updating information based on generalized credal sets. Part 3: Applications to statistical inference","authors":"Andrey G. Bronevich ,&nbsp;Igor N. Rozenberg","doi":"10.1016/j.fss.2025.109483","DOIUrl":"10.1016/j.fss.2025.109483","url":null,"abstract":"<div><div>The first and the second parts of the paper give us the theoretical foundations of updating information described by generalized credal sets.<span><span><sup>1</sup></span></span> In the third part, we will show how we can estimate parameters of probability distributions based on generalized credal sets and compare the proposed approach with the standard approaches known in statistics like the maximum likelihood method and the estimation based on confidence intervals. We also consider the estimation based on imprecise data and illustrate the powerful possibilities of generalized credal sets for describing different schemes of statistical inference.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109483"},"PeriodicalIF":3.2,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204997","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
Q-Set is not generally a topos Q-Set一般不是一个拓扑
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-05-30 DOI: 10.1016/j.fss.2025.109484
Xiao Hu, Lili Shen
{"title":"Q-Set is not generally a topos","authors":"Xiao Hu,&nbsp;Lili Shen","doi":"10.1016/j.fss.2025.109484","DOIUrl":"10.1016/j.fss.2025.109484","url":null,"abstract":"<div><div>For a commutative, unital and divisible quantale <span><math><mi>Q</mi></math></span>, it is shown that the category of <span><math><mi>Q</mi></math></span>-sets is a topos if, and only if, <span><math><mi>Q</mi></math></span> is a frame.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109484"},"PeriodicalIF":3.2,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144189962","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
Weak dual (M)-property and equality of integrals 弱对偶(M)-积分的性质与等式
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-05-28 DOI: 10.1016/j.fss.2025.109473
Wenxuan Wang, Siqi Chen, Xuanming Ye, Xiaoyang Chen, Yao Ouyang
{"title":"Weak dual (M)-property and equality of integrals","authors":"Wenxuan Wang,&nbsp;Siqi Chen,&nbsp;Xuanming Ye,&nbsp;Xiaoyang Chen,&nbsp;Yao Ouyang","doi":"10.1016/j.fss.2025.109473","DOIUrl":"10.1016/j.fss.2025.109473","url":null,"abstract":"<div><div>The weak dual (M)-property of monotone measures is introduced and its relationship with the dual (M)-property is discussed in detail. This newly introduced concept proved to be not only sufficient but also necessary for the coincidence of the pan-integral from above and the Choquet integral.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109473"},"PeriodicalIF":3.2,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168420","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
Frame-valued assembly and its applications 框值装配及其应用
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-05-28 DOI: 10.1016/j.fss.2025.109472
Mengying Liu, Yueli Yue
{"title":"Frame-valued assembly and its applications","authors":"Mengying Liu,&nbsp;Yueli Yue","doi":"10.1016/j.fss.2025.109472","DOIUrl":"10.1016/j.fss.2025.109472","url":null,"abstract":"<div><div>The aim of this paper is to use fuzzy domain theory to study some cartesian closed categories containing the category of stratified <em>L</em>-topological spaces when the truth value table <em>L</em> is a frame. Firstly, we introduce the concept of <em>L</em>-fuzzy assemblies and prove that <em>L</em>-<strong>FAssm</strong>—the category of <em>L</em>-fuzzy assemblies—is cartesian closed. <em>L</em>-<strong>FAssm</strong> contains the category of stratified <em>L</em>-topological spaces as a full and faithful subcategory. Secondly, by equipping a stratified <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-<em>L</em>-topological space with an equivalence relation, we introduce the concept of <em>L</em>-equilogical spaces and show that <em>L</em>-<strong>Equ</strong>—the category of <em>L</em>-equilogical spaces—is also cartesian closed. Then we give two categories which are equivalent to <em>L</em>-<strong>Equ</strong>. Finally, we show that there is a pair of adjoint functors between the category of <em>L</em>-fuzzy assemblies and the category of <em>L</em>-generalized convergence spaces. Further, we construct two subcategories of <em>L</em>-fuzzy assemblies satisfying certain conditions, which are equivalent to the category of <em>L</em>-Kent convergence spaces and the category of <em>L</em>-limit spaces, respectively.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109472"},"PeriodicalIF":3.2,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146334","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
Optimal weights and feasible orness of ordered weighted averaging functions in the framework of Tsallis entropy Tsallis熵框架下有序加权平均函数的最优权值和可行度
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2025-05-28 DOI: 10.1016/j.fss.2025.109471
Silvia Bortot , R.A. Marques Pereira , Anastasia Stamatopoulou
{"title":"Optimal weights and feasible orness of ordered weighted averaging functions in the framework of Tsallis entropy","authors":"Silvia Bortot ,&nbsp;R.A. Marques Pereira ,&nbsp;Anastasia Stamatopoulou","doi":"10.1016/j.fss.2025.109471","DOIUrl":"10.1016/j.fss.2025.109471","url":null,"abstract":"<div><div>We discuss the application of the maximum entropy principle to the strict weighting vectors of ordered weighted averaging functions with a given orness. The problem has been thoroughly investigated by O'Hagan, Filev and Yager, and Fullér and Majlender in the context of the classical Shannon entropy. In this paper we extend the analysis to the more general context of Tsallis entropy for positive parameter values, which reduces to Shannon entropy in the unit parameter case. In our approach, whose key element is the convenient choice of a composite Lagrange multiplier, the existence of an optimal and monotonic strict weighting vector is proven for a feasible orness interval <span><math><mo>(</mo><msubsup><mrow><mi>Ω</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>Ω</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo>)</mo></math></span> which depends on the Tsallis entropy parameter. In the small parameter domain (under unit) the feasible orness interval remains the full unit interval, as in the standard Shannon entropy case. On the other hand, in the large parameter domain (over unit) the feasible orness interval reduces to a symmetric interval around the neutral orness <span><math><mi>Ω</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span>, which gradually reduces for increasing values of the Tsallis entropy parameter.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"517 ","pages":"Article 109471"},"PeriodicalIF":3.2,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168421","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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