Search Results (262)

In intuitionistic fuzzy 2-normed spaces, there are numerous symmetries in the topological structures and mapping theorems. In this work, we present the concept of an intuitionistic fuzzy 2-normed space(IF2NS) and demonstrate its structural properties using illustrative examples. This approach unifies and broadens the scope of both classical 2-normed spaces and intuitionistic fuzzy normed spaces when specific conditions are met. We introduce the idea of fuzzy open balls and explore the convergence of sequences with respect to the topology derived from the intuitionistic fuzzy 2-norm. In addition, we define left and right N-Cauchy sequences relative to the topologies ${\tau }_N$ and ${\tau }_{N^{-1}}$ and analyze their convergence characteristics. Special attention is given to the inherent symmetry of the 2-norm, where the magnitude of a pair of vectors remains invariant under exchange of arguments, and to the balanced interaction between membership and non-membership functions in the intuitionistic fuzzy setting. This intrinsic symmetry is further reflected in the proofs of the open mapping and closed graph theorems, which naturally preserve the symmetric structure of the underlying space The paper culminates with the formulation and proof of the open mapping theorem that can be considered for its symmetric properties and the closed graph theorem in the context of IF2NS, thereby generalizing essential theorems of functional analysis to this fuzzy setting. Full article

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

The integrity parameter in vulnerability refers to a set of removed vertices and the maximum number of connected components that remain functional. A bipolar fuzzy graph (BFG) assigns membership values to both positive and negative attributes. A new parameter, integrity, is defined and discussed using an example of a BFG. The integrity value of a special type of graph is determined, and the node strength sequence (NSS) for BFG is introduced. Specific NSS values are used to discuss the integrity values of paths and cycles. The integrity of the union, join, and Cartesian product of two BFGs is presented. This parameter is then applied to a road network with both positive and negative attributes, and the findings are discussed with a conclusion. Full article

The research on the optimization and transformation of rural “production-living-ecological” functions (PLEFs) is of great significance for rural revitalization and sustainable development. Existing studies predominantly evaluate rural PLEFs at the macro level, with few micro-village case studies, and particularly empirical studies in China’s plain agricultural areas. This study takes Caiwu Village, a rural revitalization demonstration village in Yuanyang County, Henan Province, China, as a typical case. First, we constructed a village PLEF classification system based on micro-scale land use types. Then, methods such as GIS spatial analysis, actor network analysis, and satisfaction fuzzy comprehensive evaluation were comprehensively used to systematically analyze the process, mechanism, and effects of the rural PLEF transformation in Caiwu Village. Our research indicates the following: (1) Caiwu Village has gone through three stages of transformation: traditional agriculture leading, ecological agriculture starting, and agriculture-tourism integration development, indicating a shift from traditional agricultural production functions to modern production-ecological composite functions. (2) The PLEF transformation in Caiwu Village resulted from the synergy of multiple actors, including governments, cooperatives, villagers, and water-soil resources, through administrative recruitment and market recruitment. Finally, (3) there are significant differences in the effects of rural PLEF transformation based on villagers’ perception. Specifically, villagers report the highest satisfaction with ecological function, followed by living function, and the lowest satisfaction with production function. This study provides empirical evidence for understanding the differentiated transformation of PLEFs in villages in plain agricultural areas. The research results can provide decision-making references for optimizing and improving the PLEFs of Caiwu Village and other similar villages. Full article

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

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

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 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

Understanding psychological change requires a quantitative framework capable of capturing the complex and dynamic relationships among personal constructs. Personal Construct Psychology emphasizes the hierarchical reorganization of bipolar constructs, yet existing qualitative methods inadequately model the reciprocal and graded influences involved in such change. This paper introduces the Presence–Balance (PB) space, a centrality measure for constructs represented within Fuzzy Cognitive Maps (FCMs). FCMs model cognitive systems as directed, weighted graphs, allowing for nuanced analysis of construct interactions. The PB space operationalizes two orthogonal dimensions: Presence, representing the overall connectivity and activation of a construct, and Implication Balance, quantifying the directional asymmetry between influences exerted and received. By formalizing Hinkle’s hierarchical theory within a rigorous mathematical framework, the PB space enables precise identification of constructs that drive or resist transformation. This dual-dimensional model provides a structured method for analyzing personal construct systems, supporting both theoretical exploration and clinically relevant interpretations in the study of psychological change. Full article

To offer a viewpoint on convexity and connectedness inside intuitionistic fuzzy graphs (IFGs), the paper is devoted to the study of intuitionistic fuzzy geodetic convexity. The paper introduces an algorithm for precise identification and characterization of geodetic pathways in IFGs, supported by a Python program. Various properties of IF-geodetic convex sets such as IF-internal and IF-boundary vertices are obtained. Furthermore, this work introduces and characterizes the concepts of geodetic IF-cover, geodetic IF-basis, and geodetic IF-number. Additionally, the study develops the IF-geodetic Wiener index. The scope of the work explores the application of IF-geodetic cover in wireless mesh networks, focusing on the identification of gateway nodes, where symmetry in connectivity patterns enhances network efficiency. A practical implementation of the IF-geodetic Wiener index method in global human trading analysis underscores the real-world implications of the developed concepts, where the efficiency and interpretability of fuzzy geodetic measures are improved by symmetry in network topologies and trade patterns. Full article

Unsupervised feature selection aims to characterize the cluster structure of original features and select the optimal subset without label guidance. However, existing methods overlook fuzzy information in the data, failing to model cluster structures between data effectively, and rely on squared error for data reconstruction, exacerbating noise impact. Therefore, a robust unsupervised feature selection algorithm based on fuzzy anchor graphs (FWFGFS) is proposed. To address the inaccuracies in neighbor assignments, a fuzzy anchor graph learning mechanism is designed. This mechanism models the association between nodes and clusters using fuzzy membership distributions, effectively capturing potential fuzzy neighborhood relationships between nodes and avoiding rigid assignments to specific clusters. This soft cluster assignment mechanism improves clustering accuracy and the robustness of the graph structure while maintaining low computational costs. Additionally, to mitigate the interference of noise in the feature selection process, an adaptive fuzzy weighting mechanism is presented. This mechanism assigns different weights to features based on their contribution to the error, thereby reducing errors caused by redundant features and noise. Orthogonal tri-factorization is applied to the low-dimensional representation matrix. This guarantees that each center represents only one class of features, resulting in more independent cluster centers. Experimental results on 12 public datasets show that FWFGFS improves the average clustering accuracy by 5.68% to 13.79% compared with the state-of-the-art methods. Full article

In this paper, we develop a geometric formulation of datasets. The key novel idea is to formulate a dataset to be a fuzzy topological measure space as a global object and equip the space with an atlas of local charts using graphs of fuzzy linear logical functions. We call such a space a logifold. In applications, the charts are constructed by machine learning with neural network models. We implement the logifold formulation to find fuzzy domains of a dataset and to improve accuracy in data classification problems. Full article

The rapid advancement of artificial intelligence is transforming agriculture by enabling data-driven plant disease monitoring and decision support. Soil-borne mosaic wheat virus (SBWMV) is a soil-transmitted virus disease that poses a serious threat to wheat production across multiple ecological zones. Due to the regional variability in environmental conditions and symptom expressions, accurately evaluating the severity of wheat soil-borne mosaic (WSBM) infections remains a persistent challenge. To address this, the problem is formulated as large-scale group decision-making process (LSGDM), where each planting plot is treated as an independent virtual decision maker, providing its own severity assessments. This modeling approach reflects the spatial heterogeneity of the disease and enables a structured mechanism to reconcile divergent evaluations. First, for each site, field observation of infection symptoms are recorded and represented using intuitionistic fuzzy numbers (IFNs) to capture uncertainty in detection. Second, a Bayesian graph convolutional networks model (Bayesian-GCN) is used to construct a spatial trust propagation mechanism, inferring missing trust values and preserving regional dependencies. Third, an enhanced spectral clustering method is employed to group plots with similar symptoms and assessment behaviors. Fourth, a feedback mechanism is introduced to iteratively adjust plot-level evaluations based on a set of defined agricultural decision indicators sets using a multi-granulation rough set (ADISs-MGRS). Once consensus is reached, final rankings of candidate plots are generated from indicators, providing an interpretable and evidence-based foundation for targeted prevention strategies. By using the WSBM dataset collected in 2017–2018 from Walla Walla Valley, Oregon/Washington State border, the United States of America, and performing data augmentation for validation, along with comparative experiments and sensitivity analysis, this study demonstrates that the AI-driven LSGDM model integrating enhanced spectral clustering and ADISs-MGRS feedback mechanisms outperforms traditional models in terms of consensus efficiency and decision robustness. This provides valuable support for multi-party decision making in complex agricultural contexts. Full article

Graph theory models relationships by representing entities as vertices and their interactionsas edges. To handle directionality and multiple head–tail assignments, various extensions—directed, bidirected, and multidirected graphs—have been introduced, with the multidirected graph unifying the first two. In this work, we further enrich this landscape by proposing the Multidirected hypergraph, which merges the flexibility of hypergraphs and superhypergraphs to describe higher-order and hierarchical connections. Building on this, we introduce five uncertainty-aware Multidirected frameworks—fuzzy, neutrosophic, plithogenic, rough, and soft multidirected graphs—by embedding classical uncertainty models into the Multidirected setting. We outline their formal definitions, examine key structural properties, and illustrate each with examples, thereby laying groundwork for future advances in uncertain graph analysis and decision-making. Full article

The m-Polar Fuzzy Incidence Graph (m-PFIG) is an extension of the m-Polar Fuzzy Graph (m-PFG), which provides information on how vertices affect edges. This study explores the concept of matching within both bipartite and general m-polar fuzzy incidence graphs (m-PFIGs). It extends various results and theorems from fuzzy graph theory to the framework of m-PFIGs. This research investigates various operations within m-PFIGs, including augmenting paths, matching principal numbers, and the relationships among them. It focuses on identifying the most suitable employees for specific roles and achieving optimal outcomes, particularly in situations involving internal conflicts within an organization. To address fuzzy maximization problems involving vertex–incidence pairs, this study outlines key properties of maximum matching principal numbers in m-PFIGs. Ultimately, the matching concept is applied to attain these maximum principal values, demonstrating its effectiveness, particularly in bipartite m-PFIG scenarios. Full article