Fuzzy Sets and Systems最新文献

{"title":"Another view on the non-additivity index of capacity: a generalized index model and the unsupervised capacity identification with it","authors":"Kaihong Guo,&nbsp;Xueting Guan","doi":"10.1016/j.fss.2025.109569","DOIUrl":"10.1016/j.fss.2025.109569","url":null,"abstract":"<div><div>Non-additivity as a remarkable feature of non-additive measures is an important property of capacity. And the non-additivity index is a new concept presented in the current study on capacity, which gives an explicit treatment of non-additivity of a capacity and can reflect the type and degree of internal interaction among decision criteria. However, the influence and mechanism of the non-additivity index in capacity identification are still unclear for now, especially for the unsupervised learning identification methods. This paper is dedicated to an introduction of the generalized non-additivity index of capacity and an interesting unsupervised capacity identification with it, aiming to improve the quality of the modeling for the non-additivity index and reveal significant roles of the generalized index model in capacity identification with high efficiency. To start with, the definition of the generalized non-additivity index is presented, with the associated mathematical properties explored in detail. On this basis, a novel form of monotonicity constraints induced by this generalized non-additivity index is created to show the potential of improving the efficiency of capacity identification for practical purposes. This directly leads to our proposal of an interesting unsupervised capacity identification method, especially in the 2-additive case. By our technique, a desired monotone 2-additive capacity can be identified more efficiently by reducing the number of constraints from exponential to linear in the number of decision attributes, thus outperforming other sorts of methods in which a quadratic number of monotonicity constraints have to be considered. Finally, a real-world case of healthcare supplier selection is provided to attest to the practicality of our proposal.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109569"},"PeriodicalIF":2.7,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144916469","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":"Uncertainty measures in a generalized theory of evidence","authors":"Thierry Denœux","doi":"10.1016/j.fss.2025.109546","DOIUrl":"10.1016/j.fss.2025.109546","url":null,"abstract":"<div><div>Epistemic Random Fuzzy Set theory is an extension of Dempster-Shafer and possibility theories in which pieces of evidence are represented by random fuzzy sets and combined by the product-intersection rule, an extension of Dempster's rule and the product combination of possibility distributions. We propose a measure of imprecision and a measure of conflict for random fuzzy sets, uniquely characterized by minimal sets of requirements. Both measures have simple expressions involving only the contour function: in the finite case, imprecision is measured by the logarithm of the sum of the plausibilities of the singletons, while conflict is measured by the negative logarithm of the maximum plausibility over the singletons. These definitions can be easily carried over to random fuzzy sets in continuous spaces, allowing us to define the imprecision and conflict of Gaussian random fuzzy numbers and extensions. Total uncertainty is defined as the sum of imprecision and conflict. The corresponding measure, referred to as <span><math><mi>T</mi></math></span>-entropy, happens to be the min-entropy and the nonspecificity measure of, respectively, the probability distribution and the normalized possibility distribution constructed from the contour function. The application of these uncertainty measures to belief elicitation is discussed and illustrated by some examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109546"},"PeriodicalIF":2.7,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865973","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":"Improved reachable set synthesis and asynchronous quantized control for switched fuzzy systems under DoS attacks via dynamic event-triggered mechanism","authors":"Liang Zhang ,&nbsp;Quanwei Yin ,&nbsp;Ning Zhao ,&nbsp;Yongchao Liu ,&nbsp;Xinjun Wang","doi":"10.1016/j.fss.2025.109567","DOIUrl":"10.1016/j.fss.2025.109567","url":null,"abstract":"<div><div>This paper aims to study the problem of reachable set (RS) synthesis and event-driven quantization mechanism design for Takagi-Sugeno fuzzy networked switched systems with time-varying delay under denial-of-service (DoS) attacks. Firstly, an improved resilient dynamic event-triggered strategy is proposed to effectively reduce the number of signal transmissions, and suppress the adverse effects of DoS attacks. Furthermore, the fuzzy asynchronous quantization controller is constructed to further reduce the update frequency of the actuator and prolong the service life. Concurrently, considering the DoS attacks and the systems behavior, several sufficient conditions for guaranteeing system performance are derived by constructing a new multi-segmented Lyapunov functional. Then, a novel boundary lemma is proposed to determine the boundary of RS. Finally, the effectiveness and applicability of the proposed method are validated through the networked nonlinear mass-spring model.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109567"},"PeriodicalIF":2.7,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879367","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":"Optimal output feedback event-triggered tracking control for Takagi-Sugeno fuzzy systems","authors":"Wenting Song ,&nbsp;Yi Zuo ,&nbsp;Shaocheng Tong","doi":"10.1016/j.fss.2025.109565","DOIUrl":"10.1016/j.fss.2025.109565","url":null,"abstract":"<div><div>This paper studies the optimal output feedback event-triggered tracking control design problem for Takagi-Sugeno (T-S) fuzzy systems. To reduce the communication resources and controller update times, an event-triggered mechanism is designed via employing the tracking error and triggered control input signal. Based on the presented event-triggered mechanism and optimality theory, an optimal output feedback event-triggered tracking controller is developed. Since the analytical solution of the controller gains is reduced to the Agebraic Riccati Equations (AREs), which is difficult to solve directly, a Q-learning value iteration (VI) algorithm is formulated to obtain its approximation solution. It is proved that the designed optimal output feedback event-triggered tracking controller can ensure the fuzzy system to be stable and the developed Q-learning VI control algorithm is convergent. Finally, we apply the proposed optimal event-triggered output feedback control method to the truck-trailer system, the simulation and comparison results validate the effectiveness of the designed control method and its theory.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109565"},"PeriodicalIF":2.7,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861065","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":"Linear programming problem subject to bipolar max-product fuzzy relation equations with product negation","authors":"Ali Abbasi Molai","doi":"10.1016/j.fss.2025.109561","DOIUrl":"10.1016/j.fss.2025.109561","url":null,"abstract":"<div><div>In this paper, we study the linear optimization problem with bipolar max-product fuzzy relation equations and product negation. First, we investigate the structure of the solution set for its feasible domain and specify the complete solution set without explicit computation of all of its maximal and minimal solutions under a sufficient condition. In a general case, the complete solution set cannot be completely determined by a finite number of pairs of minimal and maximal solution. Hence, lower and upper bound vectors are presented for its solution set. Some sufficient conditions are also proposed to reduce the dimensions of its feasible domain. We show that each binding variable from a feasible vector can be expressed in terms of the corresponding component of the lower or upper bound vectors. Some sufficient conditions are proposed so an optimal solution for the problem exists such that each of its components is the component corresponding to the lower and upper bound vectors. A value matrix is created based on the characteristic matrix, coefficients of the objective function, and recent property. Some rules are presented to reduce the dimensions of the matrix. A modified branch-and-bound algorithm is then applied to the matrix to find the optimal solution of the problem without detecting the complete solution set of its feasible domain and comparing them. The algorithm decreases the computational complexity considerably compared with the existing algorithms for solving the problem.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109561"},"PeriodicalIF":2.7,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144842699","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":"Dual-rate security control for fuzzy singularly perturbed systems with multi-channel DoS attacks","authors":"Xiaoke Tang ,&nbsp;Dian Zhang ,&nbsp;Jun Cheng ,&nbsp;Dan Zhang ,&nbsp;Wenhai Qi ,&nbsp;Yu Fu","doi":"10.1016/j.fss.2025.109564","DOIUrl":"10.1016/j.fss.2025.109564","url":null,"abstract":"<div><div>This paper addresses the dual-rate security control for fuzzy singularly perturbed systems in the presence of denial of service (DoS) attacks. Unlike the well-known single-rate event-triggered mechanism, the dual-rate event-triggered mechanism separates the triggering conditions for fast and slow state components, optimizing data transmission and significantly reducing communication overhead. Differentiating from the Markov chain, the nonhomogeneous sojourn probability information is adopted to accurate characterize the stochastic occurrence of multi-channel DoS attacks. A novel dual-rate control strategy is also proposed, utilizing different sampling rates for fast and slow states, ensuring control effectiveness while minimizing network burden. In virtue of Lyapunov theory, the analysis for stochastic stability and conditions for controller synthesis are derived. Eventually, the effectiveness and superiority of the proposed methodology is verified through two simulation examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109564"},"PeriodicalIF":2.7,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829891","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":"Filter-induced entailment relations in paraconsistent Gödel logics","authors":"Sabine Frittella ,&nbsp;Daniil Kozhemiachenko","doi":"10.1016/j.fss.2025.109563","DOIUrl":"10.1016/j.fss.2025.109563","url":null,"abstract":"<div><div>We consider two expansions of Gödel logic <span><math><mi>G</mi></math></span> with two versions of paraconsistent negation. The first one is <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>inv</mi></mrow></msub></math></span> — the expansion of <span><math><mi>G</mi></math></span> with an <em>involuitive</em> negation <span><math><msub><mrow><mo>∼</mo></mrow><mrow><mi>i</mi></mrow></msub></math></span> defined via <span><math><mi>v</mi><mo>(</mo><msub><mrow><mo>∼</mo></mrow><mrow><mi>i</mi></mrow></msub><mi>ϕ</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>−</mo><mi>v</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></math></span>. The second one is <figure><img></figure> — an expansion with a so-called ‘strong negation’ ¬. This logic utilises <em>two independent</em> valuations on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> — <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> (support of truth or positive support) and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> (support of falsity or negative support) that are connected with ¬. Two valuations in <figure><img></figure> can be combined into one valuation <em>v</em> on <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mo>⋈</mo></mrow></msup></math></span> — the twisted product of <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with itself — with two components <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. The two logics are closely connected as <span><math><msub><mrow><mo>∼</mo></mrow><mrow><mi>i</mi></mrow></msub></math></span> and ¬ allow for similar definitions of <em>co-implication</em> — <figure><img></figure> and <figure><img></figure> — but do not coincide since the set of values of <figure><img></figure> is not ordered linearly.</div><div>Our main goal is to study different entailment relations in <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>inv</mi></mrow></msub></math></span> and <figure><img></figure> that are induced by filters on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mo>⋈</mo></mrow></msup></math></span>, respectively. In particular, we determine the exact number of such relations in both cases, establish whether any of them coincide with the entailment defined via the order on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mo>⋈</mo></mrow></msup></math></span>, and obtain their hierarchy. We also construct reductions of filter-induced entailment relations to the ones defined via the order.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109563"},"PeriodicalIF":2.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810243","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 fuzzy fractions formation","authors":"Naser Zamani ,&nbsp;Zeinab Rezaei","doi":"10.1016/j.fss.2025.109562","DOIUrl":"10.1016/j.fss.2025.109562","url":null,"abstract":"<div><div>Let <em>R</em> be a commutative ring, <em>S</em> a multiplicatively closed subset of <em>R</em> and let <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>R</mi></math></span> be the ring of fractions over <em>S</em>. For a typical fuzzy submodule <em>η</em> of the <em>R</em>-module <em>M</em>, the fuzzy fractions <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>η</mi></math></span> of <em>μ</em> is a fuzzy submodule of the <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>R</mi></math></span>-module (of fractions) <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>M</mi></math></span>. In this note, it is shown that if <span><math><mi>μ</mi><mo>⊆</mo><mi>λ</mi></math></span> are two fuzzy submodules of <em>M</em>, both having sup property, then there exist a (fuzzy sense) isomorphism between <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>λ</mi><mo>/</mo><mi>μ</mi><mo>)</mo></math></span> and <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>λ</mi><mo>/</mo><msup><mrow><mi>S</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>μ</mi></math></span>. Then, it is seen that local global principle holds true for fuzzy submodules. Furthermore, after providing some auxiliary results, it is proved that under some mild conditions, fuzzy fractions formation commutes with fuzzy residual quotient.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109562"},"PeriodicalIF":2.7,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861064","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":"Efficiency of decision rule sets in fuzzy rough set theory","authors":"Fernando Chacón-Gómez,&nbsp;M. Eugenia Cornejo,&nbsp;Jesús Medina","doi":"10.1016/j.fss.2025.109548","DOIUrl":"10.1016/j.fss.2025.109548","url":null,"abstract":"<div><div>Datasets have been interpreted in (fuzzy) rough set theory as decision tables to obtain useful information to be used, for example, in decision making. These tables have been modeled through a collection of decision rules, which was called decision algorithm by Pawlak. These algorithms are analyzed by the notion of efficiency, which evaluates their quality of classification. This paper presents two different approaches for defining the notion of efficiency in the fuzzy framework. The first approach is a direct generalization to the classical case, while the second one is focused on obtaining a bounded efficiency preserving the philosophy of the classical framework. Both approaches are illustrated by means of different properties and examples.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109548"},"PeriodicalIF":2.7,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144826621","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":"Temporally adaptive hierarchical Choquet integrals: A measure-theoretic framework for dynamic non-additive integration in approximate reasoning","authors":"Jih-Jeng Huang ,&nbsp;Chin-Yi Chen","doi":"10.1016/j.fss.2025.109550","DOIUrl":"10.1016/j.fss.2025.109550","url":null,"abstract":"<div><div>This paper introduces the Temporally Adaptive Hierarchical Choquet Integral (TAHCI), a novel theoretical framework that extends classical Choquet integration to address temporal dynamics and high-dimensional data through hierarchical structures and time-evolving fuzzy measures. We develop a rigorous measure-theoretic foundation for this framework, including a complete axiomatic characterization, uniqueness results, and preservation properties. The proposed formulation overcomes theoretical limitations of traditional models by offering tractable parameterization (reducing complexity from <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> to <span><math><mi>O</mi><mo>(</mo><mi>R</mi><mi>n</mi><mi>d</mi><mo>)</mo></math></span>, where <em>R</em> is the tensor rank, <em>n</em> is the feature dimensionality, and <em>d</em> is the hierarchy depth) while preserving key measure-theoretic properties. We establish fundamental mathematical results including convergence rates, expressivity bounds, and stability under perturbations. Our theoretical analysis reveals several novel classes of non-additive measures with unique properties that emerge from the temporal adaptation process. We characterize TAHCI's well-defined fixed points and convergence behavior under various conditions. This work advances non-additive measure theory by providing a mathematically principled approach to integrating temporal dynamics with hierarchical measure structures, with direct implications for reasoning under uncertainty and imprecision.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"520 ","pages":"Article 109550"},"PeriodicalIF":2.7,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144780243","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}