Article
Mathematics, Interdisciplinary Applications
Lian Duan, Min Shi, Chuangxia Huang, Xianwen Fang
Summary: This paper investigates the finite-time synchronization problem between two delayed and diffusive complex-valued neural networks with discontinuous activations. By designing a negative exponent controller and an adaptive control scheme, novel and useful finite-time synchronization criteria are established with an explicit estimation of the upper-bound of the settling time. The effectiveness of the theoretical analysis is substantiated through numerical simulations.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Lian Duan, Jinzhi Liu, Chuangxia Huang, Zengyun Wang
Summary: This paper focuses on the finite-/fixed-time anti-synchronization (FFTAS) problem of neural networks with leakage delays under discontinuous disturbances. By designing new negative exponential controllers and using Fillipov's theory and the Lyapunov functional method, novel FFTAS criteria are established for the considered drive-response network systems, and the corresponding settling time is estimated. The established theoretical results extend and cover the existing ones, and a numerical example is provided to verify the practicality of the obtained results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics
Hayrengul Sadik, Abdujelil Abdurahman, Rukeya Tohti
Summary: In this paper, the fixed-time synchronization problem of a type of reaction-diffusion fuzzy neural networks with stochastic perturbations is investigated using simple control schemes. Generalized fixed-time stability results for stochastic nonlinear systems are introduced, and generic fixed-time stability criteria are established. The upper bounds of settling time are directly calculated using special functions. A type of controller is designed for the fixed-time synchronization, which is simpler and more applicable. A numerical example with Matlab simulations is provided to validate the theoretical results.
Article
Automation & Control Systems
Liang Feng, Juan Yu, Cheng Hu, Chengdong Yang, Haijun Jiang
Summary: This article addresses the synchronization issue in finite and fixed time for fully complex-variable delayed neural networks with discontinuous activations and time-varying delays. By introducing a complex-valued sign function and developing two discontinuous control strategies, synchronization criteria and estimates of settling time are derived using nonsmooth analysis and novel inequality techniques in the complex field. The unified control strategy designed under a new norm framework reveals that a parameter value in the controller determines whether the networks synchronize in finite or fixed time, supported by numerical results for an example provided in the article.
IEEE TRANSACTIONS ON CYBERNETICS
(2021)
Article
Computer Science, Artificial Intelligence
Zengyun Wang, Jinde Cao, Zuowei Cai, Xuegang Tan, Rensi Chen
Summary: This study investigates the issue of finite-time synchronization of discontinuous reaction-diffusion neural networks with time-varying coefficients. The effects caused by discontinuous activations are handled by differential inclusion theory, and a relaxed Lyapunov function method is introduced to design control algorithms to achieve finite-time synchronization. The results are substantiated by two numerical simulations.
Article
Computer Science, Artificial Intelligence
Caicai Zheng, Cheng Hu, Juan Yu, Haijun Jiang
Summary: This article investigates the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) with time-varying delays. Two types of discontinuous FXT control schemes are proposed, and two forms of Lyapunov function based on p-norm and 1-norm are constructed to analyze the FXT synchronization of CNNs. By employing nonsmooth analysis and inequality techniques, simple criteria for achieving FXT synchronization and an upper bound of the settling time with less conservativeness are derived. The effect of time scale on FXT synchronization of CNNs is also considered, and numerical results for an example are provided to validate the theoretical findings.
Article
Computer Science, Artificial Intelligence
Ruoyu Wei, Jinde Cao, Sergey Gorbachev
Summary: This paper focuses on the fixed-time synchronization control of quaternion-valued memristive neural networks (QVMNNs). By decomposing the QVMNNs model into four real-valued systems and designing discontinuous control schemes based on the sign function, novel criteria for fixed-time synchronization are derived using nonsmooth analysis and inequality techniques.
COGNITIVE COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
Jian Xiao, Zhigang Zeng, Shiping Wen, Ailong Wu, Leimin Wang
Summary: This article addresses the finite-/fixed-time synchronization of delayed coupled discontinuous neural networks using novel controllers, achieving synchronization within a specified time frame. Criteria for selecting controller parameters and estimating setting time are provided based on finite-time/fixed-time theorem and Lyapunov function theory. Numerical examples demonstrate the effectiveness of the proposed control protocols.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Automation & Control Systems
Qian Wang, Lian Duan, Hui Wei, Lin Wang
Summary: This paper introduces a novel analytical method to establish new synchronization criteria for the finite-time anti-synchronization problem of delayed Hopfield neural networks with discontinuous activations. The designed controllers are independent of time delay, and the established criteria are simple to implement and explicitly estimate the upper-bound of the settling time. These findings provide a new perspective for understanding the finite-time synchronization process of discontinuous neural networks.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Automation & Control Systems
Chaouki Aouiti, Mayssa Bessifi
Summary: This article focuses on the synchronization of fuzzy Clifford-valued Cohen-Grossberg neural networks with discontinuous activations and time-varying delays. Effective conditions and a novel fixed-time convergence method are derived to ensure synchronization, with estimated settling times provided. Numerical examples with simulations confirm the effectiveness of the proposed synchronization criteria.
INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Artificial Intelligence
Zuowei Cai, Lihong Huang, Zengyun Wang
Summary: This article addresses the issue of fixed-time stability (FXTS) for discontinuous systems described by differential equations (DE) with time-varying parameters. By utilizing the tool of differential inclusion (DI) and a relaxed Lyapunov method, improved FXTS criteria and estimation formulas for settling time (SET) are derived. The novelty of the developed method lies in the indefinite derivative of the Lyapunov function. The established FXTS theorems are then applied to handle fixed-time (FXT) synchronization problems in fuzzy neural networks (FNNs) with state discontinuity, where fuzzy operations are used in synaptic law computing and a time-varying switching control protocol is designed. Moreover, a series of SET estimations for FXT synchronization are provided, and simulation examples are conducted to validate the obtained results.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
Yinjie Qian, Lian Duan, Hui Wei
Summary: This paper investigates the finite-/fixed-time synchronization problem for a class of delayed memristive reaction-diffusion neural networks (MRDNNs), and establishes novel criteria with the help of state-feedback control techniques and the finite-time stability theory.
Article
Computer Science, Artificial Intelligence
Yang Liu, Guodong Zhang, Junhao Hu
Summary: This paper mainly discusses the fixed-time stabilization and synchronization for fuzzy inertial neural networks (FINNs). By using differential inclusion theory to deal with the discontinuous system, two efficient feedback controllers are designed to ensure the FXT stabilization and synchronization of FINNs based on fixed-time stability (FTS) theories. Unlike previous studies, this paper considers the neural system model with bounded distributed delays and discontinuous activation functions. The effectiveness of the proposed methods is verified through numerical examples and simulation results.
Article
Computer Science, Artificial Intelligence
Chaouki Aouiti, Mayssa Bessifi
Summary: This paper investigates the controller design problem of synchronization in a class of Cohen-Grossberg-type fuzzy neural networks with discontinuous activation function and time-varying delays. By using theoretical analysis and numerical simulations, the efficacy of the control scheme in achieving system synchronization within bounded time and with an advantage in convergence rate is demonstrated.
NEURAL COMPUTING & APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Na Li, Xiaoqun Wu, Jianwen Feng, Yuhua Xu, Jinhu Lu
Summary: This article introduces a new lemma for fixed-time stability, which is less conservative than existing results. By utilizing simple controllers, a discontinuous neural network with mismatched parameters can synchronize to the target state within a theoretically estimated settling time, independent of initial values. The estimated settling time is closer to the real synchronization time compared to existing literature, as demonstrated through numerical simulations.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Computer Science, Theory & Methods
Irina Perfilieva, Shokrollah Ziari, Rahele Nuraei, Thi Minh Tam Pham
Summary: The proposed approach uses the F-transform to construct an operational matrix for solving the Volterra integral equation. The transformed form of the equation reduces to a system of linear equations with a triangular matrix, making the numerical method efficient and low computational. The paper provides proofs of convergence, estimation of computational complexity, and compares the results with other methods using test cases.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Yongliang Yang, Guilong Liu, Qing Li, Choon Ki Ahn
Summary: This paper proposes a novel type of Nussbaum function to handle the feedback control design problem with multiple unknown time-varying control coefficients. By separately compensating the unknown control coefficients and combining with the fixed-time stability theory, the issue of mutual cancellation is resolved and Lyapunov stability analysis becomes feasible. The theoretical discussions and simulation experiments demonstrate the effectiveness of the presented design for continuous-time stochastic nonlinear dynamical systems.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Yingfang Li, Xingxing He, Dan Meng, Keyun Qin
Summary: This paper presents an improved method for estimating the similarity between LR-type fuzzy numbers and compares it with existing methods. The proposed method overcomes the shortcomings of existing methods by considering the shape of LR-type fuzzy numbers.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Tong Kang, Leifan Yan, Long Ye, Jun Li
Summary: This note solves an open problem proposed in the paper Kang et al. (2023) [9] by demonstrating the linearity of set-valued pan-integrals based on a fuzzy measure and the operations pair (+, center dot) through the subadditivity of the fuzzy measure. It also provides an example to show the necessity of the subadditivity condition for the linearity of set-valued pan-integrals. Furthermore, it introduces the pan-integral of set-valued functions based on a fuzzy measure and pan-operations pair (circle plus, circle times).
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Marzieh Shamsizadeh, Mohammad Mehdi Zahedi, Mohamad Javad Agheli Goki
Summary: In this paper, we study a new generalization for the notion of fuzzy automata, called hesitant L-fuzzy automaton (HLFA). The mathematics framework for the theory of HLFA is presented. Moreover, the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA are introduced. Additionally, a minimal complete accessible deterministic hesitant L-fuzzy automaton is presented for recognizing any hesitant L-fuzzy language, and an algorithm is proposed to determine the states of the minimal hesitant L-fuzzy automaton along with its time complexity.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
S. O. Mashchenko
Summary: This paper investigates a fuzzy matrix game with fuzzy sets of player strategies and proposes a method to construct a game value using Zadeh's extension principle and the approach to fuzzy matrix games. It is proved that the fuzzy sets of players strategies in a fuzzy matrix game generate a game value in the form of a type-2 fuzzy set on the real line.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Gustave Bainier, Benoit Marx, Jean-Christophe Ponsart
Summary: The Nonlinear Sector Approach (NLSA) is a method to construct Takagi-Sugeno (T-S) models that precisely represent nonlinear systems with bounded nonlinearities. This paper generalizes the NLSA to polytopic and smooth convex bounding sets, providing new ways to reduce the conservatism of TS representations with interdependent scheduling parameters. Various Linear Matrix Inequalities (LMI) criteria are also provided for stability analysis of these models.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Mi Zhou, Ya-Jing Zhou, Jian-Bo Yang, Jian Wu
Summary: This study proposes a new dissimilarity measure for basic probability assignments (BPAs) in the Dempster-Shafer evidence structure, considering both distance measure and conflict belief. Comparative analysis demonstrates the applicability and validity of the proposed measure, which is further applied to multi-source data fusion and large-scale group decision making.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Nicolas Madrid, Manuel Ojeda-Aciego
Summary: This paper continues the research on the properties of the f-indexes of inclusion and contradiction, and specifically demonstrates the relationship between the two concepts through the reformulated Aristotelian square of opposition.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Hanbiao Yang, Zhongqiang Yang, Taihe Fan, Lin Yang
Summary: This paper discusses the topological structures on fuzzy numbers and their related sets, and investigates the continuity of weighted mean maps with respect to these structures. An application of the results is provided, demonstrating their practical significance.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Narayan Choudhary, S. P. Tiwari, Shailendra Singh
Summary: This paper studies different compositions of (L-fuzzy) automata using category theory and introduces four different categories for the study. It shows that each category has specific properties and advances the existing categories in the field. The monoidal description of these categories enriches the fuzzy automata theory.
FUZZY SETS AND SYSTEMS
(2024)
Article
Computer Science, Theory & Methods
Lifeng Li, Qinjun Luo
Summary: In this study, we investigate monotone comparative statics under interval uncertainty. We introduce interval-valued supermodular functions and interval-valued quasisupermodular functions with respect to a partial order relation on intervals. Moreover, we derive some sufficient conditions for monotone comparative statics under interval uncertainty. We also apply these results to analyze the monotone comparative statics of interval games with strategic complements.
FUZZY SETS AND SYSTEMS
(2024)
