Fuzzy Sets and Systems最新文献

{"title":"Approximability of triangular fuzzified nonlinear T–S fuzzy systems to p-integrable functions based on piecewise linear functions","authors":"Deli Zhang,&nbsp;Guijun Wang","doi":"10.1016/j.fss.2025.109527","DOIUrl":"10.1016/j.fss.2025.109527","url":null,"abstract":"<div><div>The piecewise linear function (PLF) is an extension of subsection linear function with one variable on Euclidean space, and it plays an important bridging role in characterizing the relationship between the fuzzy systems and the approximated function. In this article, the determinant linear expression of PLF is introduced by subdividing the input space of <em>p-</em>integral functions and solving linear equations systems, and analyzes and represents the vertex coordinates of these small polyhedrons obtained after subdivision through geometric methods. A triangular fuzzified nonlinear Takagi Sugeno (TFNL T–S) fuzzy system is established by introducing the fuzzy rules of the nonlinear output and the determinant coefficients of PLF, and it was proved through the <em>p</em>-integral norm and matrix norm that TFNL T–S fuzzy system has approximation performance for <em>p</em>-integrable functions when all parameters of a linear part in the consequents of the rules take non-zero constants. Finally, the numerical simulations were conducted on the approximation performance of TFNL T–S fuzzy systems through simulation examples. The results show that the proposed TFNL T–S fuzzy system can indeed approximate a given <em>p</em>-integrable function with arbitrary accuracy.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109527"},"PeriodicalIF":3.2,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679861","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":"Filtration-and-weighting-based triangular bounded consistency of interval-valued fuzzy preference relations","authors":"Wenjun Chang ,&nbsp;Na Zhang ,&nbsp;Huijuan Ren ,&nbsp;Chao Fu","doi":"10.1016/j.fss.2025.109524","DOIUrl":"10.1016/j.fss.2025.109524","url":null,"abstract":"<div><div>Consistency of interval-valued fuzzy preference relations (IVFPRs) is an essential property in decision-making to characterize the logic of decision-makers’ preferences. The triangular bounded consistency (TBC) of IVFPRs is a newly proposed type of consistency that corresponds to the bounded rationality of decision-makers, considering their historical preferences. The effectiveness and coherence of historical preferences should be considered to help characterize decision-makers’ real preferences under the assumption that their preferences are consistent in previous and current decision-making scenarios. To address this issue, this paper proposes a new type of consistency of IVFPRs called filtration-and-weighting-based triangular bounded consistency (FWTBC) based on the bounded rationality of decision-makers. By transforming historical IVFPRs into triangle pairs, a process of filtering abnormal triangle pairs is created based on the box plot to guarantee their effectiveness, and a process of determining the weights of the remaining triangle pairs is constructed to improve their coherence. These two processes are then integrated into the TBC of IVFPRs to generate the FWTBC of IVFPRs. A multi-criteria group decision-making method with the FWTBC of IVFPRs is presented and then applied to a thyroid biopsy needle supplier selection problem for a tertiary hospital located in Hefei City, Anhui Province, China.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109524"},"PeriodicalIF":3.2,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597611","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":"Fully distributed pinning synchronization of coupled Takagi-Sugeno fuzzy neural networks with aperiodic intermittent communication","authors":"Dan Liu ,&nbsp;Kaibo Shi ,&nbsp;Xiaohong Cui ,&nbsp;Kun Zhou ,&nbsp;Binrui Wang","doi":"10.1016/j.fss.2025.109519","DOIUrl":"10.1016/j.fss.2025.109519","url":null,"abstract":"<div><div>This article concentrates on the problem of pinning synchronization control for coupled fuzzy neural networks with aperiodic intermittent communication. To reduce the conservatism of traditional aperiodic intermittent communication schemes wherein the rest rate of each time subinterval is constrained, we introduce an average rest rate for the whole-time interval by using the concept of average dwell time. Subsequently, fully distributed pinning synchronization strategies with all-edges-based and partial-edges-based adaptive laws for coupling gains are proposed. The proposed synchronization strategies are independent of any global information, including the coupling configuration matrix and the number of coupling nodes. Within the fully distributed framework, the applicability of pinning synchronization strategies is enhanced, particularly for complex systems with large-scale and limited resources. Finally, a numerical simulation is performed to verify the validity of the derived schemes.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109519"},"PeriodicalIF":3.2,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534291","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":"Adaptive fuzzy dynamic event-triggered control for PDE-ODE cascaded systems with actuator failures","authors":"Wenxin Zhang ,&nbsp;Guangdeng Zong ,&nbsp;Ben Niu ,&nbsp;Xudong Zhao ,&nbsp;Ning Xu","doi":"10.1016/j.fss.2025.109514","DOIUrl":"10.1016/j.fss.2025.109514","url":null,"abstract":"<div><div>This paper investigates the adaptive stabilization control for partial differential equation (PDE) – ordinary differential equation (ODE) cascaded systems with actuator failures. Since the systems under consideration involve unknown nonlinear functions, fuzzy logic systems are employed to approximate these functions. Additionally, an approach combining infinite and finite-dimensional backstepping methods with adaptive dynamic compensation techniques is utilized to solve the control problem for PDE-ODE cascaded systems. Specifically, an infinite-dimensional backstepping transformation and its inverse are utilized to convert the original PDE subsystem into a target system, thereby simplifying the control design process. To further optimize the controller design, a first-order filter is incorporated into the finite-dimensional backstepping method to mitigate the “explosion of complexity” issue. Moreover, a dynamic event-triggered mechanism is introduced to save communication resources. Ultimately, the proposed control algorithm guarantees that all signals remain bounded, and this is validated through a simulation example.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109514"},"PeriodicalIF":3.2,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549108","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":"A unified weighting framework for evaluating nearest neighbour classification","authors":"Oliver Urs Lenz ,&nbsp;Henri Bollaert ,&nbsp;Chris Cornelis","doi":"10.1016/j.fss.2025.109516","DOIUrl":"10.1016/j.fss.2025.109516","url":null,"abstract":"<div><div>We present the first comprehensive and large-scale evaluation of classical (NN), fuzzy (FNN) and fuzzy rough (FRNN) nearest neighbour classification. We standardise existing proposals for nearest neighbour weighting with kernel functions, applied to the distance values and/or ranks of the nearest neighbours of a test instance. In particular, we show that the theoretically optimal Samworth weights converge to a kernel. Kernel functions are closely related to fuzzy negation operators, and we propose a new kernel based on Yager negation. We also consider various distance and scaling measures, which we show can be related to each other. Through a systematic series of experiments on 85 real-life classification datasets, we find that NN, FNN and FRNN all perform best with Boscovich distance, and that NN and FRNN perform best with a combination of Samworth rank- and distance-weights and scaling by the mean absolute deviation around the median (<span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>), the standard deviation (<span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>) or the semi-interquartile range (<span><math><msubsup><mrow><mi>r</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span>), while FNN performs best with only Samworth distance-weights and <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>- or <span><math><msub><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-scaling. However, NN achieves comparable performance with Yager-<span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> distance-weights, which are simpler to implement than a combination of Samworth distance- and rank-weights. Finally, FRNN generally outperforms NN, which in turn performs systematically better than FNN.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"519 ","pages":"Article 109516"},"PeriodicalIF":3.2,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144518000","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":"On the pointwise supremum of the set of copulas with a given curvilinear section","authors":"Yao Ouyang ,&nbsp;Yonghui Sun ,&nbsp;Hua-Peng Zhang","doi":"10.1016/j.fss.2025.109515","DOIUrl":"10.1016/j.fss.2025.109515","url":null,"abstract":"<div><div>Making use of the total variation of particular functions, we give an explicit formula for the pointwise supremum of the set of all copulas with a given curvilinear section. When the pointwise supremum is a copula is characterized. We also characterize the coincidence of the pointwise supremum and the greatest quasi-copula with the same curvilinear section.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109515"},"PeriodicalIF":3.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490127","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":"On entropies of fuzzy sets and nonlinear integrals","authors":"Rui Lv ,&nbsp;Jun Li ,&nbsp;Yuhuan Wang ,&nbsp;Zhanxin Yang","doi":"10.1016/j.fss.2025.109513","DOIUrl":"10.1016/j.fss.2025.109513","url":null,"abstract":"<div><div>This paper provides a summary of fuzzy entropies of fuzzy sets and of fuzzy measures, including the latest results in recent years on this topic. Some representative fuzzy entropies and their construction methods are shown. We focus on the discussion of using nonlinear integrals to define entropies of fuzzy sets and of fuzzy measures in continuous domain. Some new properties of the fuzzy entropies based on the Sugeno integrals and the Choquet integrals are obtained, and we briefly review three important nonlinear integrals — the concave, convex and pan-integrals, and present the latest achievements we have obtained for these integrals in recent years. We also demonstrate some new fundamental properties of convex integrals, and by means of these properties, we introduce two types of fuzzy entropies of fuzzy sets, the Knopfmacher-like and the Yager-like fuzzy entropies. In addition, we also mention our staged research results on defining the entropy of fuzzy measures via nonlinear integrals and their construction methods.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109513"},"PeriodicalIF":3.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490126","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":"Generalized unified well-posedness of equilibrium solutions for fuzzy multi-leader-multi-follower games under bounded rationality","authors":"Li Zhou ,&nbsp;Wensheng Jia","doi":"10.1016/j.fss.2025.109512","DOIUrl":"10.1016/j.fss.2025.109512","url":null,"abstract":"<div><div>In this paper, we concentrate on a new class of fuzzy multi-leader-multi-follower games with fuzzy set payoffs, abbreviated as FMLMFG, which is a fuzzy extension of the classical multi-leader-multi-follower games. First, we propose the concept of fuzzy weak Nash equilibrium (FWNE) for FMLMFG based on fuzzy sets and study the existence of FWNE. Subsequently, we formulate the bounded rationality model for FMLMFG by integrating a rationality function and study the generalized unified well-posedness (GU-wp) and unified well-posedness (U-wp). Moreover, we demonstrate the characteristics of GU-wp and U-wp for FMLMFG by utilizing the Kuratowski measure of non-compactness.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109512"},"PeriodicalIF":3.2,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321722","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":"Resilient emotional dynamics in a fuzzy happiness model: Cognitive and noncognitive perspectives","authors":"Jin Hee Yoon ,&nbsp;Youngchul Bae ,&nbsp;Sung-Kwun Oh","doi":"10.1016/j.fss.2025.109510","DOIUrl":"10.1016/j.fss.2025.109510","url":null,"abstract":"<div><div>The happiness model employs a differential equation that expresses how a person feels happy when external forces change. When a human feels a specific emotion, it is difficult to express it with a real number to describe its intensity because human emotions are ambiguous. It is more reasonable to express the degree of happiness with fuzzy numbers that can handle this ambiguity mathematically, and trapezoidal fuzzy numbers are the most suitable for this. This paper proposes an exponential function for resilience by applying the fuzzy theory. In considering a real environment, a sinusoidal function and Gaussian noise are applied when considering a real environment. In differential equations, such as the happiness model, external forces often decrease over time rather than have a constant periodicity. Thus, it may be appropriate to express the model as a resilience function that approaches zero over time. In this paper, the function representing the overall shape of the external force is defined as the forced power function expressed as an exponential function that decreases over time. The sinusoidal function, a wave function, was added as an auxiliary function, and a Gaussian noise term was added for randomness, irregularity, or noise terms. We observe the nonlinear phenomenon by expressing differential equations representing human emotions in cognitive and noncognitive states using complex fuzzy numbers and Euler’s formula. When people feel happy or sad, they cognitively know why, but in some cases, when faced with a certain situation, they may feel happier or sadder than they expected. A person’s emotions can be considered the result of a complex effect of the cognitive part, of which the person is aware, and the noncognitive state, of which the person is not aware. Complex numbers are used to represent cognitive and noncognitive states. The real part of a complex number represents the cognitive state, and the imaginary part represents the noncognitive state. Complex numbers are expressed using Euler’s formula to describe the mixed results of cognitive and noncognitive states. This paper uses a fuzzy dynamic happiness model to observe how mixed results occur in human emotions, especially nonlinear behavior. Finally, nonlinear behavior is observed through phase portraits and bifurcation diagrams for the proposed fuzzy dynamic happiness model.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109510"},"PeriodicalIF":3.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306919","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":"Many-valued aspects of tense and related operators","authors":"Michal Botur ,&nbsp;Jan Paseka ,&nbsp;Richard Smolka","doi":"10.1016/j.fss.2025.109509","DOIUrl":"10.1016/j.fss.2025.109509","url":null,"abstract":"<div><div>Our research builds upon Halmos's foundational work on functional monadic Boolean algebras and our previous work on tense operators to develop three essential constructions, including the important concepts of fuzzy sets and powerset operators. These constructions have widespread applications across contemporary mathematical disciplines, including algebra, logic, and topology. The framework we present generates four covariant and two contravariant functors, establishing three adjoint situations.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"518 ","pages":"Article 109509"},"PeriodicalIF":3.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321723","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}