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Search Results (307)

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Keywords = fuzzy boundaries

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26 pages, 5646 KB  
Article
A Symmetry-Aware BAS for Improved Fuzzy Intra-Class Distance-Based Image Segmentation
by Yazhi Wang, Lei Ding and Qing Zhang
Symmetry 2025, 17(10), 1752; https://doi.org/10.3390/sym17101752 - 17 Oct 2025
Viewed by 121
Abstract
At present, the Beetle Antennae Search (BAS) algorithm has achieved remarkable success in image segmentation. However, when dealing with some complex image segmentation problems, particularly in the context of instance segmentation, which aims to identify and delineate each distinct object of interest, even [...] Read more.
At present, the Beetle Antennae Search (BAS) algorithm has achieved remarkable success in image segmentation. However, when dealing with some complex image segmentation problems, particularly in the context of instance segmentation, which aims to identify and delineate each distinct object of interest, even within the same semantic class, there are problems such as poor optimization performance, slow convergence speed, and low stability. Therefore, to address the challenges of instance segmentation, an improved image segmentation model is proposed, and a novel BAS algorithm called the Crossover and Mutation Beetle Antennae Search (CMBAS) algorithm is designed to optimize it. The core of our approach treats instance segmentation as a sophisticated clustering problem, where each cluster center corresponds to a unique object instance. Firstly, an improved intra-class distance based on fuzzy membership weighting is designed to enhance the compactness of individual instances. Secondly, to quantify the genetic potential of individuals through their fitness performance, CMBAS uses an adaptive crossover rate mechanism based on fitness ranking and establishes a ranking-driven crossover probability allocation model. Thirdly, to guide individuals to evolve towards excellence, CMBAS uses a strategy for individual mutation of longicorn beetle antennae based on DE/current-to-best/1. Furthermore, the symmetry-aware adaptive crossover and mutation operations enhance the balance between exploration and exploitation, leading to more robust and consistent instance-level segmentation results. Experimental results on five typical benchmark functions demonstrate that CMBAS achieves superior accuracy and stability compared to the BAGWO, BAS, GWO, PSO, GA, Jaya, and FA algorithms. In image segmentation applications, CMBAS exhibits exceptional instance segmentation performance, including an enhanced ability to distinguish between adjacent or overlapping objects of the same class, resulting in smoother and more continuous instance boundaries, clearer segmented targets, and excellent convergence performance. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Intelligent Control and Computing)
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21 pages, 937 KB  
Article
FA-Seed: Flexible and Active Learning-Based Seed Selection
by Dinh Minh Vu and Thanh Son Nguyen
Information 2025, 16(10), 884; https://doi.org/10.3390/info16100884 - 10 Oct 2025
Viewed by 241
Abstract
This paper addresses the fundamental problem of seed selection in semi-supervised clustering, where the quality of initial seeds has a significant impact on clustering performance and stability. Existing methods often rely on randomly or heuristically selected seeds, which can propagate errors and increase [...] Read more.
This paper addresses the fundamental problem of seed selection in semi-supervised clustering, where the quality of initial seeds has a significant impact on clustering performance and stability. Existing methods often rely on randomly or heuristically selected seeds, which can propagate errors and increase dependence on expert labeling. To overcome these limitations, we propose FA-Seed, a flexible and adaptive model that integrates active querying with self-guided adaptation within the framework of fuzzy hyperboxes. FA-Seed partitions the data into hyperboxes, evaluates seed reliability through measures of membership and association density, and propagates labels with an emphasis on label purity. The model demonstrates strong adaptability to complex and ambiguous data distributions in which cluster boundaries are vague or overlapping. The main contributions of FA-Seed include: (1) automatic estimation and selection of candidate seeds that provide auxiliary supervision, (2) dynamic cluster expansion without retraining, (3) automatic detection and identification of structurally complex regions based on cluster characteristics, and (4) the ability to capture intrinsic cluster structures even when clusters vary in density and shape. Empirical evaluations on benchmark datasets, specifically the UCI and Computer Science collections, show that our approach consistently outperforms several state-of-the-art semi-supervised clustering methods. Full article
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24 pages, 2942 KB  
Article
A New Approach in Detecting Symmetrical Properties of the Role of Media in the Development of Key Competencies for Labor Market Positioning Using Fuzzy AHP
by Aleksandra Penjišević, Branislav Sančanin, Ognjen Bakmaz, Maja Mladenović, Branislav M. Ranđelović and Dušan J. Simjanović
Symmetry 2025, 17(10), 1645; https://doi.org/10.3390/sym17101645 - 3 Oct 2025
Viewed by 226
Abstract
The result of accelerated development and technological progress is manifested through numerous changes in the labor market, primarily concerning the competencies of future employees. Many of those competencies have symmetrical character. The determinants that may influence the development of specific competencies are variable [...] Read more.
The result of accelerated development and technological progress is manifested through numerous changes in the labor market, primarily concerning the competencies of future employees. Many of those competencies have symmetrical character. The determinants that may influence the development of specific competencies are variable and dynamic, yet they share the characteristic of transcending temporal and spatial boundaries. In this paper we propose the use of a combination of Principal Component Analysis (PCA) and Fuzzy Analytic Hierarchy Process (FAHP) to rank 21st-century competencies that are developed independently of the formal educational process. Ability to organize and plan, appreciation of diversity and multiculturalism, and ability to solve problems appeared to be the highest-ranked competencies. The development of key competencies is symmetrical to the skills for the labor market. Also, the development of key competencies is symmetrical to the right selection of the quality of media content. The paper proves that the development of key competencies is symmetrical to the level of education of both parents. One of the key findings is that participants with higher levels of media literacy express more readiness for the contemporary labor market. Moreover, the family, particularly parents, exerts a highly significant positive influence on the development of 21st-century competencies. Parents with higher levels of education, in particular, provide a stimulating environment for learning, foster critical thinking, and encourage the exploration of diverse domains of knowledge. Full article
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33 pages, 5950 KB  
Article
Fault Point Search with Obstacle Avoidance for Machinery Diagnostic Robots Using Hierarchical Fuzzy Logic Control
by Rui Mu, Ryojun Ikeura, Hongtao Xue, Chengxiang Zhao and Peng Chen
Sensors 2025, 25(19), 6127; https://doi.org/10.3390/s25196127 - 3 Oct 2025
Viewed by 307
Abstract
Higher requirements have been placed on fault detection for continuously operating machines in modern factories. Manual inspection faces challenges related to timeliness, leading to the emergence of autonomous diagnostic robots. To overcome the safety limitations of existing diagnostic robots in factory environments, a [...] Read more.
Higher requirements have been placed on fault detection for continuously operating machines in modern factories. Manual inspection faces challenges related to timeliness, leading to the emergence of autonomous diagnostic robots. To overcome the safety limitations of existing diagnostic robots in factory environments, a hierarchical fuzzy logic-based navigation and obstacle avoidance algorithm is proposed in this study. The algorithm is constructed based on zero-order Takagi–Sugeno type fuzzy control, comprising subfunctions for navigation, static obstacle avoidance, and dynamic obstacle avoidance. Coordinated navigation and equipment protection are achieved by jointly considering the information of the fault point and surrounding equipment. The concept of a dynamic safety boundary is introduced, wherein the normalized breached level is used to replace the traditional distance-based input. In the inference process for dynamic obstacle avoidance, the relative speed direction is additionally considered. A Mamdani-type fuzzy inference system is employed to infer the necessity of obstacle avoidance and determine the priority target for avoidance, thereby enabling multi-objective planning. Simulation results demonstrate that the proposed algorithm can guide the diagnostic robot to within 30 cm of the fault point while ensuring collision avoidance with both equipment and obstacles, enhancing the completeness and safety of the fault point searching process. Full article
(This article belongs to the Special Issue Feature Papers in Fault Diagnosis & Sensors 2025)
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20 pages, 3476 KB  
Article
A Quantitative Evaluation Method for Navigation Safety in Coastal Waters Based on Unstructured Grids
by Panpan Zhang, Jinqiang Bi, Xin Teng and Kexin Bao
J. Mar. Sci. Eng. 2025, 13(10), 1848; https://doi.org/10.3390/jmse13101848 - 24 Sep 2025
Viewed by 302
Abstract
In this paper, we propose a quantitative evaluation method for navigation safety in coastal waters based on unstructured grids. Initially, a comprehensive analysis was conducted on various factors affecting navigation safety, including natural conditions, traffic conditions, and marine hydro-meteorological conditions, to construct a [...] Read more.
In this paper, we propose a quantitative evaluation method for navigation safety in coastal waters based on unstructured grids. Initially, a comprehensive analysis was conducted on various factors affecting navigation safety, including natural conditions, traffic conditions, and marine hydro-meteorological conditions, to construct a multi-source fused spatiotemporal dataset. Subsequently, channel boundary extraction was performed using Constrained Delaunay Triangle–Alpha-Shapes, and the precise extraction of ship navigation areas was performed based on Constrained Delaunay Triangle–Voronoi diagrams. Additionally, temporal feature grids were constructed based on the spatiotemporal characteristics of marine hydro-meteorological data. Finally, unstructured grids for evaluating navigation safety were established through spatial overlay analysis. Based on this foundation, a quantitative analysis and evaluation model for comprehensive navigation safety assessment was developed using the fuzzy evaluation method. By calculating the fuzzy relation matrix and weight vectors, quantitative assessments were conducted for each grid cell, yielding safety risk levels from both spatial and temporal dimensions. An analysis was performed using maritime data within the geographic boundaries of lon.119.17–120.41° E and lat.34.40–35.47° N. The results indicated that the unstructured grid division and channel boundary extraction in the demonstrated sea area were closely related to parameters such as the ship traffic flow patterns and the spatiotemporal characteristics of the marine environmental factors. A quantitative evaluation and analysis of the 186 unstructured grid cells revealed that the high risk levels primarily corresponded to restricted navigation areas, the higher-risk grid cells were mainly anchorages, and the low to lower risk levels were primarily associated with channels and navigable areas for ships. Full article
(This article belongs to the Special Issue Advancements in Maritime Safety and Risk Assessment)
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28 pages, 5018 KB  
Article
Interactive Fuzzy Logic Interface for Enhanced Real-Time Water Quality Index Monitoring
by Amar Lokman, Wan Zakiah Wan Ismail, Nor Azlina Ab Aziz and Anith Khairunnisa Ghazali
Algorithms 2025, 18(9), 591; https://doi.org/10.3390/a18090591 - 21 Sep 2025
Viewed by 414
Abstract
Surface water resources are under growing pressure from urbanization, industrial activity, and agriculture, making effective monitoring essential for safeguarding ecological integrity and human use. Conventional monitoring methods, which rely on manual sampling and rigid Water Quality Index (WQI) categories, often provide delayed feedback [...] Read more.
Surface water resources are under growing pressure from urbanization, industrial activity, and agriculture, making effective monitoring essential for safeguarding ecological integrity and human use. Conventional monitoring methods, which rely on manual sampling and rigid Water Quality Index (WQI) categories, often provide delayed feedback and oversimplify conditions near classification thresholds, limiting their usefulness for timely management. To overcome these shortcomings, we have developed an interactive fuzzy logic-based water quality monitoring interface or dashboard that integrates the WQI developed by Malaysia’s Department of Environment with the National Water Quality Standards (NWQS) Class I–V framework. The interface combines conventional WQI computation with advanced visualization tools such as dynamic gauges, parameter tables, fuzzy membership graphs, scatter plots, heatmaps, and bar charts. Then, triangular membership functions map six key parameters to NWQS classes, providing smoother and more nuanced interpretation compared to rigid thresholds. In addition to that, the dashboard enables clearer communication of trends, supports timely decision-making, and demonstrates adaptability for broader applications since it is implemented on the Replit platform. Finally, evaluation results show that the fuzzy interface improves interpretability by resolving ambiguities in over 15% of cases near class boundaries and facilitates faster assessment of pollution trends compared to conventional reporting. Thus, these contributions highlight the necessity and value of the research on advancing Malaysia’s national water quality monitoring and providing a scalable framework for international contexts. Full article
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31 pages, 7404 KB  
Article
Multi-Stage Coordinated Azimuth Control for High-Precision Balloon-Borne Astronomical Platforms
by Yulang Cui, Jianghua Zhou, Yijian Li, Wanning Huang and Yongqi Liu
Aerospace 2025, 12(9), 821; https://doi.org/10.3390/aerospace12090821 - 11 Sep 2025
Viewed by 415
Abstract
This study investigates multi-level coupled dynamic issues in near-space balloon-borne astronomical observation platforms subjected to multi-source disturbances, proposing an integrated azimuth pointing control scheme combining unified modeling with composite control strategies. A nonlinear dynamic model is established to characterize inertial coupling effects between [...] Read more.
This study investigates multi-level coupled dynamic issues in near-space balloon-borne astronomical observation platforms subjected to multi-source disturbances, proposing an integrated azimuth pointing control scheme combining unified modeling with composite control strategies. A nonlinear dynamic model is established to characterize inertial coupling effects between the gondola system and secondary gimbal platform. The velocity-loop feedback mechanism utilizing fiber-optic gyroscopes achieves base disturbance decoupling, while an adaptive fuzzy PID controller enhances position-loop disturbance rejection capabilities. A gain adaptation strategy coordinates hierarchical control dynamics, complemented by anti-windup constraints safeguarding actuator operational boundaries. Simulation verifications confirm the exceptional high-precision pointing capability and robust stability under representative wind disturbances and sensor noise conditions. The system maintains a superior control performance across parameter perturbation scenarios, demonstrating consistent operational reliability. This study provides an innovative technical paradigm for precision observation missions in near space. Full article
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24 pages, 840 KB  
Article
Adaptive Event-Triggered Full-State Constrained Control of Multi-Agent Systems Under Cyber Attacks
by Jinxia Wu, Pengfei Cui, Juan Wang and Yuanxin Li
Actuators 2025, 14(9), 448; https://doi.org/10.3390/act14090448 - 11 Sep 2025
Viewed by 402
Abstract
For multi-agent systems under Denial-of-Service (DoS) attacks, a relative threshold strategy for event triggering and a state-constrained control method with prescribed performance are proposed. Within the framework of combining graph theory with the leader–follower approach, coordinate transformation is utilized to decouple the multi-agent [...] Read more.
For multi-agent systems under Denial-of-Service (DoS) attacks, a relative threshold strategy for event triggering and a state-constrained control method with prescribed performance are proposed. Within the framework of combining graph theory with the leader–follower approach, coordinate transformation is utilized to decouple the multi-agent system. Inspired by the three-way handshake technology of TCP communication, a DoS detection system is designed based on event-triggering. This system is used to detect DoS attacks, prevent the impacts brought by DoS attacks, and reduce the update frequency of the controller. Fuzzy logic systems are employed to approximate the unknown nonlinear functions within the system. By using a first-order filter to approximate the derivative of the virtual controller, the computational complexity issue in the backstepping method is addressed. Furthermore, The Barrier Lyapunov Function (BLF) possesses unique mathematical properties. When the system state approaches the pre-set boundary, it can exhibit a special variation trend, thereby imposing a restrictive effect on the system state. The Prescribed Performance Function (PPF), on the other hand, defines the expected performance standards that the system aims to achieve in the tracking task, covering key indicators such as tracking accuracy and response speed. By organically integrating these two functions, the system can continuously monitor and adjust its own state during operation. When there is a tendency for the tracking error to deviate from the specified range, the combined function mechanism will promptly come into play. Through the reasonable adjustment of the system’s control input, it ensures that the tracking error always remains within the pre-specified range. Finally, through Lyapunov analysis, the proposed control protocol ensures that all closed-loop signals remain bounded under attacks, with the outputs of all followers synchronizing with the leader’s output in the communication graph. Full article
(This article belongs to the Special Issue Advanced Technologies in Actuators for Control Systems)
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15 pages, 3677 KB  
Article
Contextual Feature Expansion with Superordinate Concept for Compositional Zero-Shot Learning
by Soohyeong Kim and Yong Suk Choi
Appl. Sci. 2025, 15(17), 9837; https://doi.org/10.3390/app15179837 - 8 Sep 2025
Viewed by 480
Abstract
Compositional Zero-Shot Learning (CZSL) seeks to enable machines to recognize objects and attributes (i.e., primitives),learn their associations, and generalize to novel compositions, enabling systems to exhibit a human-like ability to infer and generalize. The existing approaches, multi-label and multi-class classification, face inherent trade-offs: [...] Read more.
Compositional Zero-Shot Learning (CZSL) seeks to enable machines to recognize objects and attributes (i.e., primitives),learn their associations, and generalize to novel compositions, enabling systems to exhibit a human-like ability to infer and generalize. The existing approaches, multi-label and multi-class classification, face inherent trade-offs: the former suffers from biases against unrelated compositions, while the latter struggles with exponentially growing search spaces as the number of objects and attributes increases. To overcome these limitations and address the exponential complexity in CZSL, we introduce Concept-oriented Feature ADjustment (CoFAD), a novel method that extracts superordinate conceptual features based on primitive relationships and expands label feature boundaries. By incorporating spectral clustering and membership function in fuzzy logic, CoFAD achieves state-of-the-art performance while using 2×–4× less GPU memory and reducing training time by up to 50× on large-scale dataset. Full article
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19 pages, 17084 KB  
Article
SPADE: Superpixel Adjacency Driven Embedding for Three-Class Melanoma Segmentation
by Pablo Ordóñez, Ying Xie, Xinyue Zhang, Chloe Yixin Xie, Santiago Acosta and Issac Guitierrez
Algorithms 2025, 18(9), 551; https://doi.org/10.3390/a18090551 - 2 Sep 2025
Viewed by 593
Abstract
The accurate segmentation of pigmented skin lesions is a critical prerequisite for reliable melanoma detection, yet approximately 30% of lesions exhibit fuzzy or poorly defined borders. This ambiguity makes the definition of a single contour unreliable and limits the effectiveness of computer-assisted diagnosis [...] Read more.
The accurate segmentation of pigmented skin lesions is a critical prerequisite for reliable melanoma detection, yet approximately 30% of lesions exhibit fuzzy or poorly defined borders. This ambiguity makes the definition of a single contour unreliable and limits the effectiveness of computer-assisted diagnosis (CAD) systems. While clinical assessment based on the ABCDE criteria (asymmetry, border, color, diameter, and evolution), dermoscopic imaging, and scoring systems remains the standard, these methods are inherently subjective and vary with clinician experience. We address this challenge by reframing segmentation into three distinct regions: background, border, and lesion core. These regions are delineated using superpixels generated via the Simple Linear Iterative Clustering (SLIC) algorithm, which provides meaningful structural units for analysis. Our contributions are fourfold: (1) redefining lesion borders as regions, rather than sharp lines; (2) generating superpixel-level embeddings with a transformer-based autoencoder; (3) incorporating these embeddings as features for superpixel classification; and (4) integrating neighborhood information to construct enhanced feature vectors. Unlike pixel-level algorithms that often overlook boundary context, our pipeline fuses global class information with local spatial relationships, significantly improving precision and recall in challenging border regions. An evaluation on the HAM10000 melanoma dataset demonstrates that our superpixel–RAG–transformer (region adjacency graph) pipeline achieves exceptional performance (100% F1 score, accuracy, and precision) in classifying background, border, and lesion core superpixels. By transforming raw dermoscopic images into region-based structured representations, the proposed method generates more informative inputs for downstream deep learning models. This strategy not only advances melanoma analysis but also provides a generalizable framework for other medical image segmentation and classification tasks. Full article
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30 pages, 81237 KB  
Article
Quantification of Overlapping and Network Complexity in News: Assessment of Top2Vec and Fuzzy Topic Models
by Ismail Burak Parlak, Musa Şervan Şahin, Tankut Acarman, Mouloud Adel and Salah Bourennane
Appl. Sci. 2025, 15(17), 9627; https://doi.org/10.3390/app15179627 - 1 Sep 2025
Viewed by 536
Abstract
Topic modeling in digital news faces the dual challenge of thematic overlap and evolving semantic boundaries, especially in morphologically rich languages like Turkish. To address these obstacles, we propose a topic modeling framework enhanced with knowledge graphs that explicitly incorporates uncertainty in topic [...] Read more.
Topic modeling in digital news faces the dual challenge of thematic overlap and evolving semantic boundaries, especially in morphologically rich languages like Turkish. To address these obstacles, we propose a topic modeling framework enhanced with knowledge graphs that explicitly incorporates uncertainty in topic assignment. We focus on the diversity of Fuzzy Latent Semantic Analysis (FLSA) and compare the performance with Latent Dirichlet Allocation (LDA), BERTopic, and embedding-based Top2Vec on a corpus drawn from two Turkish news agencies. We evaluate each model using standard metrics for topic coherence, diversity, and interpretability. We propose Shannon entropy of node-degree distributions to measure the network complexity of knowledge graphs as topic similarity. Our results indicate that FLSA achieves perfect topic diversity, 1.000 and improved interpretability, 0.33 over LDA, 0.09 while also enhancing coherence, 0.33 vs. 0.27. Top2Vec demonstrates the strongest coherence, 0.81 and interpretability, 0.78 with high diversity, 0.97, reflecting its capacity to form semantically cohesive clusters. Entropy analysis further shows that FLSA produces the most information-rich topic networks. These findings suggest that fuzzy modeling and embedding-based approaches offer complementary strengths, uncertainty-aware flexibility, and semantic precision, thereby improving topic discovery in complex, unstructured news environments. Full article
(This article belongs to the Special Issue Machine Learning-Based Feature Extraction and Selection: 2nd Edition)
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21 pages, 3235 KB  
Article
RetinalCoNet: Underwater Fish Segmentation Network Based on Bionic Retina Dual-Channel and Multi-Module Cooperation
by Jianhua Zheng, Yusha Fu, Junde Lu, Jinfang Liu, Zhaoxi Luo and Shiyu Zhang
Fishes 2025, 10(9), 424; https://doi.org/10.3390/fishes10090424 - 27 Aug 2025
Viewed by 443
Abstract
Underwater fish image segmentation is the key technology to realizing intelligent fisheries and ecological monitoring. However, the problems of light attenuation, blurred boundaries, and low contrast caused by complex underwater environments seriously restrict the segmentation accuracy. In this paper, RetinalConet, an underwater fish [...] Read more.
Underwater fish image segmentation is the key technology to realizing intelligent fisheries and ecological monitoring. However, the problems of light attenuation, blurred boundaries, and low contrast caused by complex underwater environments seriously restrict the segmentation accuracy. In this paper, RetinalConet, an underwater fish segmentation network based on bionic retina dual-channel and multi-module cooperation, is proposed. Firstly, the bionic retina dual-channel module is embedded in the encoder to simulate the separation and processing mechanism of light and dark signals by biological vision systems and enhance the feature extraction ability of fuzzy target contours and translucent tissues. Secondly, the dynamic prompt module is introduced, and the response of key features is enhanced by inputting adaptive prompt templates to suppress the noise interference of water bodies. Finally, the edge prior guidance mechanism is integrated into the decoder, and low-contrast boundary features are dynamically enhanced by conditional normalization. The experimental results show that RetinalCoNet is superior to other mainstream segmentation models in the key indicators of mDice, reaching 82.3%, and mIou, reaching 89.2%, and it is outstanding in boundary segmentation in many different scenes. This study achieves accurate fish segmentation in complex underwater environments and contributes to underwater ecological monitoring. Full article
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21 pages, 3369 KB  
Article
Event-Triggered Fixed-Time Consensus Tracking Control for Uncertain Nonlinear Multi-Agent Systems with Dead-Zone Input
by Zian Wang, Yixiang Gu, Jiarui Liu, Yue Zhang, Kai Feng, Jietao Dai and Guoxiong Zheng
Actuators 2025, 14(9), 414; https://doi.org/10.3390/act14090414 - 22 Aug 2025
Viewed by 724
Abstract
This study explores the issue of fixed-time dynamic event-triggered consensus control for uncertain nonlinear multi-agent systems (MASs) within directed graph frameworks. In practical applications, the system encounters multiple constraints such as unknown time-varying parameters, unknown external disturbances, and input dead zones, which may [...] Read more.
This study explores the issue of fixed-time dynamic event-triggered consensus control for uncertain nonlinear multi-agent systems (MASs) within directed graph frameworks. In practical applications, the system encounters multiple constraints such as unknown time-varying parameters, unknown external disturbances, and input dead zones, which may increase the communication burden of the system. Therefore, achieving fixed-time consensus tracking control under the aforementioned conditions is challenging. To address these issues, an adaptive fixed-time consensus tracking control method based on boundary estimation and fuzzy logic systems (FLSs) is proposed to achieve online compensation for the input dead zone. Additionally, to optimize the utilization of communication resources, a periodic adaptive event-triggered control (PAETC) is designed. The mechanism dynamically adjusts the frequency at which the trigger is updated in real time, reducing communication resource usage by responding to changes in the control signal. Finally, the efficacy of the proposed approach is confirmed via theoretical evaluation and simulation. Full article
(This article belongs to the Special Issue Analysis and Design of Linear/Nonlinear Control System)
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16 pages, 301 KB  
Article
Solutions of Nonlinear Differential and Integral Equations via Optimality Results Involving Proximal Mappings
by Sonam, Deb Sarkar, Purvee Bhardwaj, Satyendra Narayan and Ramakant Bhardwaj
AppliedMath 2025, 5(3), 108; https://doi.org/10.3390/appliedmath5030108 - 22 Aug 2025
Viewed by 373
Abstract
This research paper delves into the application of optimality results in orthogonal fuzzy metric spaces to demonstrate the existence and uniqueness of solutions of nonlinear differential equations with boundary conditions and nonlinear integral equations, emphasizing the importance of orthogonal fuzzy metric spaces in [...] Read more.
This research paper delves into the application of optimality results in orthogonal fuzzy metric spaces to demonstrate the existence and uniqueness of solutions of nonlinear differential equations with boundary conditions and nonlinear integral equations, emphasizing the importance of orthogonal fuzzy metric spaces in extending fixed-point theory. Through introducing this innovative concept, the study provides a theoretical framework for analyzing mappings in diverse scenarios. In this study, we introduce the concept of best proximity point (BPP) within the framework of orthogonal fuzzy metric spaces by employing orthogonal fuzzy proximal contractive mappings. Moreover, this research explores the implications of the established results, considering both self-mappings and non-self mappings that share the same parameter set. Additionally, some examples are provided to illustrate the practical relevance of the proven results and consequences in various mathematical contexts. The findings of this study can open up avenues for further exploration and application in solving real-world problems. Full article
29 pages, 3058 KB  
Article
Existence, Uniqueness, and Stability of Weighted Fuzzy Fractional Volterra–Fredholm Integro-Differential Equation
by Sahar Abbas, Abdul Ahad Abro, Syed Muhammad Daniyal, Hanaa A. Abdallah, Sadique Ahmad, Abdelhamied Ashraf Ateya and Noman Bin Zahid
Fractal Fract. 2025, 9(8), 540; https://doi.org/10.3390/fractalfract9080540 - 16 Aug 2025
Viewed by 577
Abstract
This paper investigates a novel class of weighted fuzzy fractional Volterra–Fredholm integro-differential equations (FWFVFIDEs) subject to integral boundary conditions. The analysis is conducted within the framework of Caputo-weighted fractional calculus. Employing Banach’s and Krasnoselskii’s fixed-point theorems, we establish the existence and uniqueness of [...] Read more.
This paper investigates a novel class of weighted fuzzy fractional Volterra–Fredholm integro-differential equations (FWFVFIDEs) subject to integral boundary conditions. The analysis is conducted within the framework of Caputo-weighted fractional calculus. Employing Banach’s and Krasnoselskii’s fixed-point theorems, we establish the existence and uniqueness of solutions. Stability is analyzed in the Ulam–Hyers (UHS), generalized Ulam–Hyers (GUHS), and Ulam–Hyers–Rassias (UHRS) senses. A modified Adomian decomposition method (MADM) is introduced to derive explicit solutions without linearization, preserving the problem’s original structure. The first numerical example validates the theoretical findings on existence, uniqueness, and stability, supplemented by graphical results obtained via the MADM. Further examples illustrate fuzzy solutions by varying the uncertainty level (r), the variable (x), and both parameters simultaneously. The numerical results align with the theoretical analysis, demonstrating the efficacy and applicability of the proposed method. Full article
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