{"title":"Fixed-time self-triggered fuzzy adaptive control of N-link robotic manipulators","authors":"","doi":"10.1016/j.fss.2024.109134","DOIUrl":"10.1016/j.fss.2024.109134","url":null,"abstract":"<div><div>This paper studies the fixed-time fuzzy adaptive self-triggered control of <em>n</em>-link robotic manipulators. To achieve fixed-time stability, a fuzzy adaptive fixed-time control algorithm is proposed by reconstructing the self-triggered controller and using the singularity-free function, which avoids the singularity problem and obtains fixed-time stability. Meanwhile, the self-triggered mechanism reduces the communication resources between the actuator and the controller, improving the system's transmission efficiency. Through the above thoughts, a kind of fixed-time fuzzy adaptive controller based on the self-triggered mechanism is designed, which guarantees that the tracking error of each joint converges to the prescribed range within a fixed time. Finally, the effectiveness of the proposed algorithm is verified by a simulation example of the two-link robotic manipulator.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326925","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}
{"title":"Quasi-D-overlap functions: Construction and characterization","authors":"","doi":"10.1016/j.fss.2024.109138","DOIUrl":"10.1016/j.fss.2024.109138","url":null,"abstract":"<div><div>In this paper, we mainly consider the construction and characterization of so-called quasi-<em>D</em>-overlap functions, which are derived from <em>D</em>-overlap functions and irreducible quasi-D-overlap functions proposed by the author lately. The main contributions are: (i) it presents the concept of quasi-<em>D</em>-overlap functions and obtains construction manner of them by means of matrixes; (ii) it illustrates the relationship between quasi-<em>D</em>-overlap functions and 1-Lipschitz semi-quasi-overlap functions; (iii) it gives equivalent characterization of quasi-<em>D</em>-overlap functions and proper quasi-<em>D</em>-overlap functions by dint of matrixes, moreover, it obtains that the convex combination of quasi-<em>D</em>-overlap functions is also a quasi-<em>D</em>-overlap function.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326926","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}
{"title":"Isomorphic triangular subnorms with continuous additive generators","authors":"","doi":"10.1016/j.fss.2024.109136","DOIUrl":"10.1016/j.fss.2024.109136","url":null,"abstract":"<div><div>The additive generators play an important role in the construction of t-(sub)norms. Distinct to t-norms, the additive generators of t-subnorms need not be strictly decreasing and the value at 1 need not be 0. This paper gives the sufficient and necessary conditions such that two t-subnorms, generated by continuous additive generators, are isomorphic.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326927","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}
{"title":"Multi-view evidential c-means clustering with view-weight and feature-weight learning","authors":"","doi":"10.1016/j.fss.2024.109135","DOIUrl":"10.1016/j.fss.2024.109135","url":null,"abstract":"<div><div>Multi-view clustering remains a challenging task due to the potential overlap of clusters and variability across different views, which causes uncertainty and imprecision in cluster assignment. This paper explores multi-view evidential <em>c</em>-means clustering with view-weight and feature-weight learning (MVECM-VFL), grounded in the theory of belief functions (TBF). The aim is to effectively capture the uncertainty and imprecision in cluster assignment while concurrently assessing the contributions of view and feature weights in the clustering framework. We integrate view and feature weights and credal partition into a joint learning framework and design a new objective function to find the best results. In MVECM-VFL, each object can belong to different clusters with various masses of belief, thereby characterizing the uncertainty. Furthermore, when an object resides in the overlapping area of several singleton clusters, it can be attributed to a meta-cluster (defined as the union of these singleton clusters) to represent the local imprecision in cluster assignment. Additionally, view-weight and feature-weight learning can help to obtain the credal partition better. Compared to the related methods, the effectiveness of MVECM-VFL is demonstrated based on synthetic and real-world datasets.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314592","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}
{"title":"Topology on residuated lattices for biresiduum-based continuity of fuzzy sets","authors":"","doi":"10.1016/j.fss.2024.109133","DOIUrl":"10.1016/j.fss.2024.109133","url":null,"abstract":"<div><div>By continuity of <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>-valued fuzzy set it is usually understood standard continuity of a real-valued function. This could be in conflict with the similarity fuzzy relation on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> given by the operation of biresiduum induced by a left-continuous t-norm. In this work, a new kind of continuity, called t-continuity, of an <em>L</em>-set in a topological space for <em>L</em> being a complete residuated lattice of finite dimension is defined. It is based on a notion of oscillation of <em>L</em>-set, which is an element of <em>L</em> computed by means of biresiduum in <em>L</em>. A topology on <em>L</em> of this continuity, called the t-topology on <em>L</em>, is found. This topology is constructed by means of biresiduum and a variant of Scott-open sets called residuated Scott-open sets. It is shown that the t-topology of <em>L</em> is Hausdorff and that <em>L</em> together with its t-topology is a topological residuated lattice. T-topologies of four standard t-norms are found. The notion of t-topology is generalized to sets with <em>L</em>-equivalence relation and a new characteristic of extensional sets implying that extensional <em>L</em>-sets are t-continuous is given.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311541","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}
{"title":"Disturbance observer-based nonsingular fixed-time fuzzy adaptive event-triggered output feedback control of uncertain nonlinear systems","authors":"","doi":"10.1016/j.fss.2024.109132","DOIUrl":"10.1016/j.fss.2024.109132","url":null,"abstract":"<div><div>This article examines the fuzzy adaptive event-triggered output feedback control issue of eliminating fixed-time singularity for a type of uncertain nonlinear systems with disturbance observer structures. By introducing novel bounded time-varying functions (TVFs), a set of more general intermediate-variable-based disturbance observers (IVBDOs) is constructed. Combining the corresponding auxiliary reduced-power function and the quartic Lyapunov method, a co-design scheme for a fuzzy approximation high-order controller and an improved event-triggered mechanism with a judgment indicator threshold is proposed. Especially, the developed framework not only removes the singularity during the fixed-time design process but also further reduces the communication resources. By means of theoretical analysis, the devised solution achieves fixed-time stable control (FTSC) of the system and the tracking error converges to the desired neighborhood around the origin. After verifying the absence of Zeno behavior, the efficacy of the presented methodology is supported by two simulation examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142320250","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}
{"title":"Scott algebraic closure space and its applications","authors":"","doi":"10.1016/j.fss.2024.109127","DOIUrl":"10.1016/j.fss.2024.109127","url":null,"abstract":"<div><p>In this paper, we want to use the idea of fuzzy topological space generated by classical topological space to study generated algebraic closure space and its applications. Firstly, we show that the generated <span><math><mtext>Q</mtext></math></span>-Scott open set monad induced by classical Scott open set monad is a submonad of <span><math><mtext>Q</mtext></math></span>-Scott open set monad if and only if the underlying partial order of the quantale <span><math><mtext>Q</mtext></math></span> is a frame. Then, we give a reasonable explanation for constructing Scott algebraic closure system on a frame <span><math><mtext>Q</mtext></math></span> since it plays a similar role as Scott topology in topology. Finally, by the Scott algebraic closure system, we construct a monad on the category of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> separated algebraic closure spaces and show that the Eilenberg-Moore algebras of this monad are precisely frames.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242389","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}
{"title":"Intermittent dynamic event-triggered control for synchronization of Takagi–Sugeno fuzzy competitive neural networks with leakage delay and different time scales","authors":"","doi":"10.1016/j.fss.2024.109130","DOIUrl":"10.1016/j.fss.2024.109130","url":null,"abstract":"<div><p>Because competitive neural networks (CNNs) can simulate the phenomena of lateral inhibition among neurons, their dynamics are attracting increasing attention, which motives us to investigate the global exponential synchronization issue of multiple time-delays fuzzy CNNs (MDFCNNs) with different time scales in this article. Firstly, to solve the significant resource wastage problem caused by the time-triggered mechanism previously adopted in CNNs, a novel intermittent dynamic event-triggered mechanism is proposed. It is worth mentioning that the fuzzy logic systems are also utilized in this model and controller, effectively handling the uncertainties and nonlinearities in practical problems. Secondly, by designing the intermittent static/dynamic event-triggered mechanism, we derive the global exponential synchronization conditions for MDFCNNs with different time scales under a simpler and more implementable controller composed of a linear negative feedback control term. We also utilize the reduction to absurdity to demonstrate the nonexistence of Zeno behavior for the error system of master-slave CNNs. Furthermore, we provide several corollaries to further indicate the generality of the model and the cost savings of the control mechanism. Finally, we provide an example and some comparisons to demonstrate the efficiency of the derived theoretical findings.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242388","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}
{"title":"Antitone involutions on tensor products of complete lattices and complete distributivity","authors":"","doi":"10.1016/j.fss.2024.109131","DOIUrl":"10.1016/j.fss.2024.109131","url":null,"abstract":"<div><p>The purpose of this paper is to study antitone involutions on tensor products of complete lattices. A lattice with antitone involution is called an involution lattice. We show that if <em>M</em> is a completely distributive involution lattice, then for each complete involution lattice <em>L</em> there exists a <em>unique</em> antitone involution on the tensor product <span><math><mi>M</mi><mo>⊗</mo><mi>L</mi></math></span> such that the natural embeddings of <em>M</em> and <em>L</em> into <span><math><mi>M</mi><mo>⊗</mo><mi>L</mi></math></span> are involution-preserving. This is best possible, since the described property characterizes complete distributivity in the class of complete involution lattices. When <em>M</em> and <em>L</em> are completely distributive involution lattices, <span><math><mi>M</mi><mo>⊗</mo><mi>L</mi></math></span> with the aforementioned antitone involution is the codomain of a universal bimorphism in the sense of the category of all completely distributive de Morgan algebras and their join- and involution-preserving maps. The case that <em>M</em> and <em>L</em> are orthocomplemented is explored too.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016501142400277X/pdfft?md5=b339827f1904818ee8c165a4985654c2&pid=1-s2.0-S016501142400277X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242390","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}
{"title":"On Ralescu's cardinality of fuzzy sets","authors":"","doi":"10.1016/j.fss.2024.109118","DOIUrl":"10.1016/j.fss.2024.109118","url":null,"abstract":"<div><p>We provide a direct formula for Ralescu's scalar cardinality. Unlike the original, iterative definition, the formula reveals intuitive shortcomings of this concept of cardinality. These are apparent from examples and reflected formally in that, as we show, the concept violates one of the axioms of cardinality of fuzzy sets. In addition, we provide a relationship of this concept to Ralescu's concept of fuzzy cardinality which unveils a tight link between the two concepts and points out another counterintuitive property of the concept of scalar cardinality. We argue that the discussed concept of fuzzy cardinality represents an interesting proposition, suggest its geometric interpretation, and provide preliminary observations as a basis for future considerations.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136550","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}