Article
Mathematics, Interdisciplinary Applications
Nattakan Boonsatit, Santhakumari Rajendran, Chee Peng Lim, Anuwat Jirawattanapanit, Praneesh Mohandas
Summary: The issue of adaptive finite-time cluster synchronization for neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A new adaptive control technique is developed to achieve finite-time synchronization of the networks. The effectiveness of the proposed method is demonstrated through simulation studies.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Artificial Intelligence
Qiwei Liu, Huaicheng Yan, Hao Zhang, Chaoyang Chen, Yufang Chang
Summary: This article addresses the exponential synchronization problem for a class of fuzzy inertial memsirtor-based neural networks with mixed time-varying delays. First, the inertial items are described as second-order systems and transformed into first-order systems by utilizing a appropriate variable substitution. Then, the fuzzy state-feedback control strategy and fuzzy adaptive control strategy are designed to ensure the exponential synchronization under the framework of Filippov solutions. The exponential synchronization algebraic conditions are obtained by choosing a proper Lyapunov-Krasovskii functional. Finally, two numerical simulations are provided to validate the effectiveness and benefit of the proposed results.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Shuzhan Wang, Ziye Zhang, Chong Lin, Jian Chen
Summary: This paper investigates the fixed-time synchronization of complex-valued BAM neural networks with time-varying delays using pinning control and adaptive control. The proposed methods improve communication efficiency, control performance, and automatically adjust control parameters for better synchronization. The results are validated through numerical examples demonstrating effectiveness and feasibility.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Information Systems
Meng Hui, Ning Yao, Herbert Ho-Ching Iu, Rui Yao, Lin Bai
Summary: This paper investigates the adaptive synchronization of fractional-order complex-valued neural networks with time-varying delays (FOCVNNTDs). Two novel fractional-order differential inequalities with time delays are established, which extend the Halanay inequality. By using a novel adaptive controller based on these inequalities, the complete synchronization and quasi-projective synchronization of FOCVNNTDs are achieved. A non-decomposition method is adopted to study the adaptive synchronization of FOCVNNTDs, which avoids the complexity of theoretical analysis.
Article
Mathematics, Applied
Runan Guo, Shengyuan Xu
Summary: This paper investigates the synchronization problem of complex-valued inertial neural networks using sliding mode control (SMC). The study considers both mixed time-varying delays and unknown control disturbances. The systems are analyzed in the complex domain due to the absence of equivalent transformations of real- and complex-valued systems. A disturbance observer is designed to estimate the unknown control disturbance. A delay-dependent synchronization criterion is proposed based on linear matrix inequality technique using suitable integral switching surface function and innovative Lyapunov-Krasovskii functionals. An efficient SMC law based on the disturbance observer is designed, and the accessibility analysis of the predefined switching surface is provided. Numerical verification based on two types of activation functions, as well as superiority and practicability analysis, are also provided.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics
Yujuan Tian, Yuhan Yin, Fei Wang, Kening Wang
Summary: This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks under an impulsive controller, proposing stability criteria in terms of complex-valued linear matrix inequalities and a new impulsive differential inequality to address the difficulties caused by mixed time delays and delayed impulse effects. An illustrative example is provided to support the theoretical results.
Article
Mathematics, Applied
Xiaofeng Wei, Ziye Zhang, Chong Lin, Jian Chen
Summary: This article studies the synchronization and anti-synchronization problems of complex-valued inertial neural networks with time-varying delays. By expressing the network model as a first-order complex-valued differential system and using Lyapunov functional and LMIs approach, sufficient conditions for synchronization and anti-synchronization are established. Numerical examples are provided to demonstrate the effectiveness of the proposed results.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Interdisciplinary Applications
R. Perumal, M. Hymavathi, M. Syed Ali, Batul A. A. Mahmoud, Waleed M. Osman, Tarek F. Ibrahim
Summary: This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions for stability of the proposed networks are established using discrete fractional calculus, discrete Laplace transform, and fractional-order discrete Mittag-Leffler functions. Adequate criteria for global asymptotic stability are determined using Lyapunov's direct technique, Lyapunov approach, and novel analysis techniques of fractional calculation. Some sufficient conditions are obtained to guarantee global stability. The theoretical results are demonstrated using numerical examples.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Artificial Intelligence
Yin Sheng, Haoyu Gong, Zhigang Zeng
Summary: This paper investigates global synchronization of complex-valued neural networks (CVNNs) with unbounded time-varying delays. An algebraic criterion is established to ensure global synchronization of the CVNNs via a devised feedback controller, which generalizes some existing outcomes, by applying analytical method and inequality techniques. Finally, two numerical simulations and one application in image encryption are provided to verify the effectiveness of the theoretical results.
Article
Mathematics, Applied
Shuang Li, Xiao-mei Wang, Hong-ying Qin, Shou-ming Zhong
Summary: This paper investigates the synchronization problem of neutral-type quaternion-valued neural networks with mixed delays. Linear and nonlinear feedback controllers are proposed to study global and finite-time synchronization, respectively. Sufficient conditions for synchronization are obtained based on appropriate functional and synchronization techniques, with less conservative results than existing ones shown through numerical examples.
Article
Engineering, Mechanical
Runan Guo, Junwei Lu, Yongmin Li, Wenshun Lv
Summary: This paper investigates the problem of fixed-time synchronization for delayed complex-valued neural networks with inertial term, proposing two different controllers that can achieve perfect synchronization in a fixed time for networks with different types of activation functions. Synchronization criteria in terms of matrix inequalities and estimates of the settling times are derived, utilizing innovative inequalities in the complex field, representing an advancement of existing research progress. Numerical simulations for various types of activation functions are provided to support the theoretical results.
NONLINEAR DYNAMICS
(2021)
Article
Automation & Control Systems
Runan Guo, Shengyuan Xu, Jian Guo
Summary: This work explores the synchronization problem of two nonidentical complex-valued inertial neural networks considering time-varying delays, leakage delay, and external disturbances. It proposes an integral sliding-mode surface suitable for the system and designs efficient sliding-mode control laws. By constructing innovative Lyapunov-Krasovskii functionals, the synchronization criteria are obtained in the forms of linear matrix inequality techniques.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Neurosciences
Yufei Liu, Bo Shen, Jie Sun
Summary: This paper proposes a class of complex-valued neural networks with stochastic parameters and mixed time delays and investigates their stability and synchronization. The numerical examples demonstrate the effectiveness of the proposed theoretical results.
COGNITIVE NEURODYNAMICS
(2023)
Article
Automation & Control Systems
Jianwen Feng, Jingxin Chen, Jingyi Wang, Yi Zhao
Summary: This paper investigates the exponential synchronization problem for complex networks with hybrid delays using the event intermittent control (EIC) strategy. A modified lemma related to delays is derived without pre-designing intermittent instants, and synchronization criteria with less conservatism are established using linear matrix inequalities (LMIs). The effectiveness of the proposed EIC strategy is verified through simulations of a numerical example.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Theory & Methods
Pan Wang, Xuechen Li, Nan Wang, Yuanyuan Li, Kaibo Shi, Jianquan Lu
Summary: This paper studies the synchronization issue of quaternion-valued fuzzy cellular neural networks (QVFCNNs) with leakage delays by decomposing them into an analogous real-valued system and investigating the existence of almost periodic solutions based on the Banach fixed point theorem. A novel state-feedback controller is designed to ensure the synchronization of global exponential almost periodicity. The effectiveness of the results is illustrated through two examples.
FUZZY SETS AND SYSTEMS
(2022)
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)