Pub Date : 2024-11-15DOI: 10.1016/j.fss.2024.109194
Linh Anh Nguyen
<div><div>Nondeterministic fuzzy transition systems (NFTSs) offer a robust framework for modeling and analyzing systems with inherent uncertainties and imprecision, which are prevalent in real-world scenarios. Wu et al. (2018) provided an algorithm for computing the crisp bisimilarity (the greatest crisp bisimulation) of a finite NFTS <span><math><mi>S</mi><mo>=</mo><mo>〈</mo><mi>S</mi><mo>,</mo><mi>A</mi><mo>,</mo><mi>δ</mi><mo>〉</mo></math></span>, with a time complexity of order <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>⋅</mo><mo>|</mo><mi>δ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> under the assumption that <span><math><mo>|</mo><mi>δ</mi><mo>|</mo><mo>≥</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span>. Qiao et al. (2023) provided an algorithm for computing the fuzzy bisimilarity (the greatest fuzzy bisimulation) of a finite NFTS <span><math><mi>S</mi></math></span> under the Gödel semantics, with a time complexity of order <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>⋅</mo><mo>|</mo><mi>δ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mi>l</mi><mo>)</mo></math></span> under the assumption that <span><math><mo>|</mo><mi>δ</mi><mo>|</mo><mo>≥</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span>, where <em>l</em> is the number of fuzzy values used in <span><math><mi>S</mi></math></span> plus 1. In this work, we provide efficient algorithms for computing the partition corresponding to the crisp bisimilarity of a finite NFTS <span><math><mi>S</mi></math></span>, as well as the compact fuzzy partition corresponding to the fuzzy bisimilarity of <span><math><mi>S</mi></math></span> under the Gödel semantics. Their time complexities are of the order <span><math><mi>O</mi><mo>(</mo><mo>(</mo><mrow><mi>size</mi></mrow><mo>(</mo><mi>δ</mi><mo>)</mo><mi>log</mi><mo></mo><mi>l</mi><mo>+</mo><mo>|</mo><mi>S</mi><mo>|</mo><mo>)</mo><mi>log</mi><mo></mo><mo>(</mo><mo>|</mo><mi>S</mi><mo>|</mo><mo>+</mo><mo>|</mo><mi>δ</mi><mo>|</mo><mo>)</mo><mo>)</mo></math></span>, where <em>l</em> is the number of fuzzy values used in <span><math><mi>S</mi></math></span> plus 2. When <span><math><mo>|</mo><mi>δ</mi><mo>|</mo><mo>≥</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span>, this order is within <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><mo>|</mo><mo>⋅</mo><mo>|</mo><mi>δ</mi><mo>|</mo><mo>⋅</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo></mo><mo>|</mo><mi>δ</mi><mo>|</mo><mo>)</mo></math></span>. The reduction of time complexity from <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>⋅</mo><mo>|</mo><mi>δ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> and <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><m
非确定性模糊过渡系统（NFTS）为建模和分析具有内在不确定性和不精确性的系统提供了一个稳健的框架，而这种不确定性和不精确性在现实世界的场景中非常普遍。Wu等人（2018）提供了一种计算有限NFTS S=〈S,A,δ〉的干脆二相似度（最大干脆二拟合）的算法，在|δ|≥|S||的假设下，时间复杂度为O(|S|4⋅|δ|2)阶。乔等人（2023）提供了一种在哥德尔语义下计算有限 NFTS S 的模糊二相似度（最大模糊二拟合）的算法，在假设|δ|≥|S|的情况下，时间复杂度为阶 O(|S|4⋅|δ|2⋅l)，其中 l 是 S 中使用的模糊值数加 1。在这项工作中，我们提供了计算与有限 NFTS S 的清晰相似性相对应的分区以及与哥德尔语义下 S 的模糊相似性相对应的紧凑模糊分区的高效算法。它们的时间复杂度为 O((size(δ)logl+|S|)log(|S|+|δ|))，其中 l 是 S 中使用的模糊值数加 2。当|δ≥||S|时，这个阶次在 O(|S|⋅|δ|⋅log2|δ|) 以内。时间复杂度从 O(|S|4⋅|δ|2) 和 O(|S|4⋅|δ|2⋅l) 降低到 O(|S|⋅|δ|⋅log2|δ|) 是这项工作的重大贡献。
{"title":"Efficient algorithms for computing bisimulations for nondeterministic fuzzy transition systems","authors":"Linh Anh Nguyen","doi":"10.1016/j.fss.2024.109194","DOIUrl":"10.1016/j.fss.2024.109194","url":null,"abstract":"<div><div>Nondeterministic fuzzy transition systems (NFTSs) offer a robust framework for modeling and analyzing systems with inherent uncertainties and imprecision, which are prevalent in real-world scenarios. Wu et al. (2018) provided an algorithm for computing the crisp bisimilarity (the greatest crisp bisimulation) of a finite NFTS <span><math><mi>S</mi><mo>=</mo><mo>〈</mo><mi>S</mi><mo>,</mo><mi>A</mi><mo>,</mo><mi>δ</mi><mo>〉</mo></math></span>, with a time complexity of order <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>⋅</mo><mo>|</mo><mi>δ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> under the assumption that <span><math><mo>|</mo><mi>δ</mi><mo>|</mo><mo>≥</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span>. Qiao et al. (2023) provided an algorithm for computing the fuzzy bisimilarity (the greatest fuzzy bisimulation) of a finite NFTS <span><math><mi>S</mi></math></span> under the Gödel semantics, with a time complexity of order <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>⋅</mo><mo>|</mo><mi>δ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mi>l</mi><mo>)</mo></math></span> under the assumption that <span><math><mo>|</mo><mi>δ</mi><mo>|</mo><mo>≥</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span>, where <em>l</em> is the number of fuzzy values used in <span><math><mi>S</mi></math></span> plus 1. In this work, we provide efficient algorithms for computing the partition corresponding to the crisp bisimilarity of a finite NFTS <span><math><mi>S</mi></math></span>, as well as the compact fuzzy partition corresponding to the fuzzy bisimilarity of <span><math><mi>S</mi></math></span> under the Gödel semantics. Their time complexities are of the order <span><math><mi>O</mi><mo>(</mo><mo>(</mo><mrow><mi>size</mi></mrow><mo>(</mo><mi>δ</mi><mo>)</mo><mi>log</mi><mo></mo><mi>l</mi><mo>+</mo><mo>|</mo><mi>S</mi><mo>|</mo><mo>)</mo><mi>log</mi><mo></mo><mo>(</mo><mo>|</mo><mi>S</mi><mo>|</mo><mo>+</mo><mo>|</mo><mi>δ</mi><mo>|</mo><mo>)</mo><mo>)</mo></math></span>, where <em>l</em> is the number of fuzzy values used in <span><math><mi>S</mi></math></span> plus 2. When <span><math><mo>|</mo><mi>δ</mi><mo>|</mo><mo>≥</mo><mo>|</mo><mi>S</mi><mo>|</mo></math></span>, this order is within <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><mo>|</mo><mo>⋅</mo><mo>|</mo><mi>δ</mi><mo>|</mo><mo>⋅</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo></mo><mo>|</mo><mi>δ</mi><mo>|</mo><mo>)</mo></math></span>. The reduction of time complexity from <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>4</mn></mrow></msup><mo>⋅</mo><mo>|</mo><mi>δ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> and <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>S</mi><msup><mrow><m","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109194"},"PeriodicalIF":3.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703352","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 : 2024-11-15DOI: 10.1016/j.fss.2024.109195
Haiyu Pan , Jie Zhou , Yuming Lin , Yongzhi Cao
Fuzzy model checking, also called multi-valued model checking, has proved to be an effective technique in verifying properties of fuzzy systems. One important issue with fuzzy model checking, is that a model adopted in fuzzy model checking is frequently updated with small changes, and it is too costly to run a model-checking algorithm from scratch in response to every update. To address the issue, in this paper, we consider the incremental model-checking approach for fuzzy systems by making maximal use of previous model checking results or in other words, by minimizing unnecessary recomputation. The models of our study are fuzzy Kripke structures, which are a fuzzy counterpart of Kripke structures and used to describe fuzzy systems, while the properties of fuzzy systems are expressed using fuzzy computation tree logic, a fuzzy temporal logic derived from computation tree logic. The focus of the paper is on how to design incremental model-checking algorithms for two until-formulas which characterize the maximal or dually minimum constrained reachability properties with respect to fuzzy Kripke structures under transition insertions or deletions but not both. The feasibility of our approach is illustrated by an example arising from the path planning problem of mobile robots.
{"title":"Incremental model checking for fuzzy computation tree logic","authors":"Haiyu Pan , Jie Zhou , Yuming Lin , Yongzhi Cao","doi":"10.1016/j.fss.2024.109195","DOIUrl":"10.1016/j.fss.2024.109195","url":null,"abstract":"<div><div>Fuzzy model checking, also called multi-valued model checking, has proved to be an effective technique in verifying properties of fuzzy systems. One important issue with fuzzy model checking, is that a model adopted in fuzzy model checking is frequently updated with small changes, and it is too costly to run a model-checking algorithm from scratch in response to every update. To address the issue, in this paper, we consider the incremental model-checking approach for fuzzy systems by making maximal use of previous model checking results or in other words, by minimizing unnecessary recomputation. The models of our study are fuzzy Kripke structures, which are a fuzzy counterpart of Kripke structures and used to describe fuzzy systems, while the properties of fuzzy systems are expressed using fuzzy computation tree logic, a fuzzy temporal logic derived from computation tree logic. The focus of the paper is on how to design incremental model-checking algorithms for two until-formulas which characterize the maximal or dually minimum constrained reachability properties with respect to fuzzy Kripke structures under transition insertions or deletions but not both. The feasibility of our approach is illustrated by an example arising from the path planning problem of mobile robots.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109195"},"PeriodicalIF":3.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703350","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 : 2024-11-14DOI: 10.1016/j.fss.2024.109193
Diego Castaño , José Patricio Díaz Varela , Gabriel Savoy
The axiomatic system introduced by Hájek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom and the infinitary rule to achieve strong completeness with respect to continuous t-norms.
{"title":"Strong completeness for the predicate logic of the continuous t-norms","authors":"Diego Castaño , José Patricio Díaz Varela , Gabriel Savoy","doi":"10.1016/j.fss.2024.109193","DOIUrl":"10.1016/j.fss.2024.109193","url":null,"abstract":"<div><div>The axiomatic system introduced by Hájek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom <span><math><msup><mrow><mo>(</mo><mo>∀</mo><mi>x</mi><mi>ϕ</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>↔</mo><mo>∀</mo><mi>x</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and the infinitary rule<span><span><span><math><mfrac><mrow><mi>ϕ</mi><mo>∨</mo><mo>(</mo><mi>α</mi><mo>→</mo><msup><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>:</mo><mi>n</mi><mo>∈</mo><mi>N</mi></mrow><mrow><mi>ϕ</mi><mo>∨</mo><mo>(</mo><mi>α</mi><mo>→</mo><mi>α</mi><mi>&</mi><mi>β</mi><mo>)</mo></mrow></mfrac></math></span></span></span> to achieve strong completeness with respect to continuous t-norms.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109193"},"PeriodicalIF":3.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703348","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}
This study emanates from a simple observation: as specified by Vapnik [37] in his study, an artificial neural network cannot generate a universal approximator if the aggregation function chosen to design the artificial neuron does not include non-linearity. The usual option is to follow a linear aggregation by a non-linear function, or so-called activation function. We wonder if this approach could be replaced by one using a natively non-linear aggregation function.
Among all of the available non-linear aggregation functions, here we are interested in aggregations based on weighted minimum and weighted maximum operations [8]. As these operators were originally developed within a possibility theory and fuzzy rule framework, such operators cannot be easily integrated into a neural network because the values that are usually considered belong to . For gradient descent based learning, a neuron must be an aggregation function derivable with respect to its inputs and synaptic weights, whose variables (synaptic weights, inputs and outputs) must all be signed real values. We thus propose an extension of weighted maximum based aggregation to enable this learning process. We show that such an aggregation can be seen as a combination of four Sugeno integrals. Finally, we compare this type of approach with the classical one.
{"title":"Combining thresholded real values for designing an artificial neuron in a neural network","authors":"Olivier Strauss , Agnès Rico , Jérôme Pasquet , Lionel Pibre","doi":"10.1016/j.fss.2024.109191","DOIUrl":"10.1016/j.fss.2024.109191","url":null,"abstract":"<div><div>This study emanates from a simple observation: as specified by Vapnik <span><span>[37]</span></span> in his study, an artificial neural network cannot generate a universal approximator if the aggregation function chosen to design the artificial neuron does not include non-linearity. The usual option is to follow a linear aggregation by a non-linear function, or so-called activation function. We wonder if this approach could be replaced by one using a natively non-linear aggregation function.</div><div>Among all of the available non-linear aggregation functions, here we are interested in aggregations based on weighted minimum and weighted maximum operations <span><span>[8]</span></span>. As these operators were originally developed within a possibility theory and fuzzy rule framework, such operators cannot be easily integrated into a neural network because the values that are usually considered belong to <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. For gradient descent based learning, a neuron must be an aggregation function derivable with respect to its inputs and synaptic weights, whose variables (synaptic weights, inputs and outputs) must all be signed real values. We thus propose an extension of weighted maximum based aggregation to enable this learning process. We show that such an aggregation can be seen as a combination of four Sugeno integrals. Finally, we compare this type of approach with the classical one.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109191"},"PeriodicalIF":3.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663949","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}
Pub Date : 2024-11-13DOI: 10.1016/j.fss.2024.109173
Marcin Kolenda , Filip Strobin , Kamil Wiśniewski
We consider versions of the chaos game algorithm for generating attractors of fuzzy iterated function systems (FIFSs for short). We show that a naive approach fails in a general setting of contractive FIFSs and we present its natural modifications that work in all cases. Our approach bases on certain modifications of orbits and shadings of a given FIFS, generated by disjunctive drivers. To complete the picture, we present also a version of the deterministic algorithm.
{"title":"Chaos game algorithm for fuzzy iterated function systems","authors":"Marcin Kolenda , Filip Strobin , Kamil Wiśniewski","doi":"10.1016/j.fss.2024.109173","DOIUrl":"10.1016/j.fss.2024.109173","url":null,"abstract":"<div><div>We consider versions of the chaos game algorithm for generating attractors of fuzzy iterated function systems (FIFSs for short). We show that a naive approach fails in a general setting of contractive FIFSs and we present its natural modifications that work in all cases. Our approach bases on certain modifications of orbits and shadings of a given FIFS, generated by disjunctive drivers. To complete the picture, we present also a version of the deterministic algorithm.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"500 ","pages":"Article 109173"},"PeriodicalIF":3.2,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142703347","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 : 2024-11-12DOI: 10.1016/j.fss.2024.109176
Feiyue Shen , Haoyi Zhang , Wenhai Qi , Ju H. Park , Jun Cheng , Kaibo Shi
This paper studies the nonfragile anti-transitional-asynchrony fault tolerant control for discrete interval type-2 fuzzy semi-Markov jump systems with bounded dwell time. In contrast to the traditional Takagi-Sugeno (T-S) fuzzy model, this paper utilises the interval 2-type fuzzy model to represent the nonlinear discrete semi-Markov jump systems. The main novelty is to design an anti-transitional-asynchrony fault-tolerant control mechanism with controller gain fluctuations under the framework of IT2 fuzzy, fault-tolerant control, and transitional asynchrony, which reduces the conservatism to a certain extent. The transitional asynchrony is adopted, i.e., the controller switching lags behind the plant switching, and this lag is associated with the transition between the current mode and the next mode. By virtue of semi-Markov kernel method, the mean-square stability of the underlying system is achieved, overcoming the difficulties caused by the transitional asynchrony. In addition, taking into account that the actuator may encounter random faults during system operation, this paper applies a fault tolerant method in the design of nonfragile anti-transitional-asynchrony control to improve the fault tolerance of the system. Finally, a tunnel circuit model verifies the effectiveness of the designed control method.
{"title":"Nonfragile anti-transitional-asynchrony fault tolerant control for IT2 fuzzy semi-Markov jump systems with actuator failures","authors":"Feiyue Shen , Haoyi Zhang , Wenhai Qi , Ju H. Park , Jun Cheng , Kaibo Shi","doi":"10.1016/j.fss.2024.109176","DOIUrl":"10.1016/j.fss.2024.109176","url":null,"abstract":"<div><div>This paper studies the nonfragile anti-transitional-asynchrony fault tolerant control for discrete interval type-2 fuzzy semi-Markov jump systems with bounded dwell time. In contrast to the traditional Takagi-Sugeno (T-S) fuzzy model, this paper utilises the interval 2-type fuzzy model to represent the nonlinear discrete semi-Markov jump systems. The main novelty is to design an anti-transitional-asynchrony fault-tolerant control mechanism with controller gain fluctuations under the framework of IT2 fuzzy, fault-tolerant control, and transitional asynchrony, which reduces the conservatism to a certain extent. The transitional asynchrony is adopted, i.e., the controller switching lags behind the plant switching, and this lag is associated with the transition between the current mode and the next mode. By virtue of semi-Markov kernel method, the mean-square stability of the underlying system is achieved, overcoming the difficulties caused by the transitional asynchrony. In addition, taking into account that the actuator may encounter random faults during system operation, this paper applies a fault tolerant method in the design of nonfragile anti-transitional-asynchrony control to improve the fault tolerance of the system. Finally, a tunnel circuit model verifies the effectiveness of the designed control method.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109176"},"PeriodicalIF":3.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663944","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 : 2024-11-12DOI: 10.1016/j.fss.2024.109171
Siyu Guo, Yingnan Pan, Zhechen Zhu
This paper considers the prescribed performance fuzzy adaptive tracking control problem of multiagent systems under a chaos-based privacy-preserving mechanism and a learning-enabled event-triggered mechanism. Initially, a chaos-based mask function is constructed, which is related to the chaotic states in the Lorentz system. The utilization of chaos adds unpredictability and full randomness to the mask function, which greatly reduces the risk of privacy leakage. Additionally, two value functions are designed as inputs of the fully connected neural network, and the fully connected neural network is used to predict the parameter value in the event-triggered mechanism, which effectively enhances the flexibility of the proposed learning-enabled event-triggered mechanism. Furthermore, in the process of controller design, by employing an error transformed function, the system errors are stabilized within the prescribed performance boundaries. Finally, a simulation example is provided to validate the effectiveness of the proposed control scheme.
{"title":"Learning-enabled event-triggered fuzzy adaptive control of multiagent systems with prescribed performance: A chaos-based privacy-preserving method","authors":"Siyu Guo, Yingnan Pan, Zhechen Zhu","doi":"10.1016/j.fss.2024.109171","DOIUrl":"10.1016/j.fss.2024.109171","url":null,"abstract":"<div><div>This paper considers the prescribed performance fuzzy adaptive tracking control problem of multiagent systems under a chaos-based privacy-preserving mechanism and a learning-enabled event-triggered mechanism. Initially, a chaos-based mask function is constructed, which is related to the chaotic states in the Lorentz system. The utilization of chaos adds unpredictability and full randomness to the mask function, which greatly reduces the risk of privacy leakage. Additionally, two value functions are designed as inputs of the fully connected neural network, and the fully connected neural network is used to predict the parameter value in the event-triggered mechanism, which effectively enhances the flexibility of the proposed learning-enabled event-triggered mechanism. Furthermore, in the process of controller design, by employing an error transformed function, the system errors are stabilized within the prescribed performance boundaries. Finally, a simulation example is provided to validate the effectiveness of the proposed control scheme.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109171"},"PeriodicalIF":3.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663946","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 : 2024-11-12DOI: 10.1016/j.fss.2024.109189
Samira Fatemi, Ildar Sadeqi, Fridoun Moradlou
We give the concept of subdifferentiability for a fuzzy n-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.
我们给出了模糊 n 单元数值函数的次微分性概念。然后，我们根据新定义阐述了与次微分性相关的一些定理。最后，我们介绍了优化问题的一些应用，包括拉格朗日对偶问题和复合最小化问题。
{"title":"Subdifferential of fuzzy n-cell number-valued functions and its applications in optimization problems","authors":"Samira Fatemi, Ildar Sadeqi, Fridoun Moradlou","doi":"10.1016/j.fss.2024.109189","DOIUrl":"10.1016/j.fss.2024.109189","url":null,"abstract":"<div><div>We give the concept of subdifferentiability for a fuzzy <em>n</em>-cell number-valued function. Then we state some theorems related to the subdifferentiability based on the new definition. Finally, we present some applications focused on optimization problems, including the Lagrangian dual problem and the composite minimization problem.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109189"},"PeriodicalIF":3.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663947","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 : 2024-11-08DOI: 10.1016/j.fss.2024.109180
Yang Wu, Lianjun Hu, Qi Chen, Yong Zhang, Libing Wu
This paper focuses on the problem of dynamic event-triggered fault-tolerant control (FTC) for nonaffine systems with unmeasurable state and asymmetric error constrain. At first, an adaptive failure compensation observer is designed to calculate unpredictable state of the nonaffine systems. Then, a dynamic event triggering strategy (DETS) is constructed to adjust the control signal and make it more flexible in transmission. Next, a new error-dependent conversion function (EDCF) is designed to confine tracing error, which can ensure that the designed Lyapunov function is always positive definite, and extend the symmetric constraint boundary to the asymmetric constraint boundary. The tracking performance and stability of closed-loop systems are proven through Lyapunov stability analysis. Finally, the availability of this method is verified by simulation experiments.
{"title":"Dynamic event-triggered fault-tolerant control for nonaffine systems with asymmetric error constraint","authors":"Yang Wu, Lianjun Hu, Qi Chen, Yong Zhang, Libing Wu","doi":"10.1016/j.fss.2024.109180","DOIUrl":"10.1016/j.fss.2024.109180","url":null,"abstract":"<div><div>This paper focuses on the problem of dynamic event-triggered fault-tolerant control (FTC) for nonaffine systems with unmeasurable state and asymmetric error constrain. At first, an adaptive failure compensation observer is designed to calculate unpredictable state of the nonaffine systems. Then, a dynamic event triggering strategy (DETS) is constructed to adjust the control signal and make it more flexible in transmission. Next, a new error-dependent conversion function (EDCF) is designed to confine tracing error, which can ensure that the designed Lyapunov function is always positive definite, and extend the symmetric constraint boundary to the asymmetric constraint boundary. The tracking performance and stability of closed-loop systems are proven through Lyapunov stability analysis. Finally, the availability of this method is verified by simulation experiments.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109180"},"PeriodicalIF":3.2,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663943","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 : 2024-11-08DOI: 10.1016/j.fss.2024.109188
Bin Pang , Xiu-Yun Wu , Bernard De Baets
Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that axiomatic properties of ternary fuzzy relations seem to be ideally suited to capture geometric characteristics of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as geometric properties. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.
{"title":"Geometric properties of ternary fuzzy relations","authors":"Bin Pang , Xiu-Yun Wu , Bernard De Baets","doi":"10.1016/j.fss.2024.109188","DOIUrl":"10.1016/j.fss.2024.109188","url":null,"abstract":"<div><div>Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that <em>axiomatic properties</em> of ternary fuzzy relations seem to be ideally suited to capture <em>geometric characteristics</em> of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as <em>geometric properties</em>. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"499 ","pages":"Article 109188"},"PeriodicalIF":3.2,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663945","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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