Fuzzy Graphs: Theory and Applications

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 March 2024) | Viewed by 4054

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Department of Computer and Information Sciences, Northumbria University, Newcastle-upon-Tyne, UK
Interests: mathematics; complex systems; networks; computer science; physics
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Guest Editor
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
Interests: graphs; graph theory; fuzzy graph theory; chemical graph theory; spectral graph theory

Special Issue Information

Dear Colleagues,

Fuzzy graphs are a powerful mathematical framework that extends traditional graph theory to accommodate uncertainty and imprecision. In contrast to conventional graphs where relationships between nodes are binary, fuzzy graphs allow for the representation of gradual, non-binary associations. This abstract explores the fundamental concepts and applications of fuzzy graphs in various domains. Fuzzy graphs find applications in diverse fields, including social network analysis, image processing, transportation optimization, medical diagnosis, and decision-making. They offer a robust means of capturing complex relationships and quantifying uncertainty, making them invaluable in scenarios where traditional crisp data models fall short. Fuzzy graph-based algorithms enable more nuanced data analysis and decision support, contributing to improved problem-solving in real-world applications. This abstract aims to provide a brief insight into the world of fuzzy graphs, highlighting their importance in handling imprecise data and modeling intricate relationships. As an evolving field at the intersection of mathematics, computer science, and applied sciences, fuzzy graphs continue to drive innovation and enhance our ability to tackle complex problems in an uncertain world. The concept of fuzzy graphs has enriched our capacity to model and analyze complex systems in the presence of uncertainty and imprecision. Their applications span a wide spectrum of fields, contributing to more realistic and effective solutions. This abstract only scratches the surface of the potential of fuzzy graphs, highlighting their significance in addressing real-world challenges across various domains. As we delve deeper into this fascinating field, we uncover new ways to harness the power of fuzzy graphs for a more nuanced understanding of the world around us. The applications of fuzzy graphs are multifaceted and extend across numerous domains:

  1. Social Networks: In the age of social media and online interactions, modeling the strength of connections between individuals is vital. Fuzzy graphs enable us to represent the varying degrees of friendship or influence within a network, offering more realistic social network analysis;
  2. Transportation and Logistics: Fuzzy graphs find extensive use in optimizing transportation networks. They allow for the representation of imprecise data, such as traffic congestion levels or variable travel times, enabling better route planning and resource allocation;
  3. Medical Diagnosis: Healthcare decisions often involve uncertain and imprecise data. Fuzzy graphs can model medical conditions and their relationships, aiding in diagnostic processes that consider the degrees of symptom severity and disease likelihood;
  4. Image Processing: Fuzzy graph-based algorithms play a crucial role in image segmentation, edge detection, and pattern recognition. They can handle images with varying degrees of feature significance and noise;
  5. Decision Support Systems: In decision-making scenarios, where factors are not always clear-cut, fuzzy graphs assist by modeling the imprecision in data. This is particularly valuable in fields such as finance, where risk assessment and portfolio management benefit from fuzzy modeling;
  6. Natural Language Processing: Fuzzy graphs enhance the representation of linguistic information, facilitating the development of more context-aware language models and sentiment analysis tools;
  7. Environmental Modeling: Environmental systems often involve imprecise data, and fuzzy graphs help in modeling ecological networks and predicting environmental changes with greater accuracy.

Dr. Yilun Shang
Dr. Zeeshan Saleem Mufti
Guest Editors

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Keywords

  • graph theory and its applications
  • fuzzy graphs and their applications
  • fuzzy graphs with machine learning
  • fuzzy logic
  • fuzzy graphs in different fields of science (name some of them)
  • fuzzy graphs with AI

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Published Papers (2 papers)

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Research

16 pages, 607 KiB  
Article
A Novel Domination in Vague Influence Graphs with an Application
by Xiaolong Shi, Ruiqi Cai, Ali Asghar Talebi, Masomeh Mojahedfar and Chanjuan Liu
Axioms 2024, 13(3), 150; https://doi.org/10.3390/axioms13030150 - 26 Feb 2024
Viewed by 1301
Abstract
Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In [...] Read more.
Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In this paper, we present the domination concept for VIG. Some issues and results of the domination in vague graphs (VGs) are also developed in VIGs. We defined some basic notions in the VIGs such as the walk, path, strength of In-pair , strong In-pair, In-cut vertex, In-cut pair (CP), complete VIG and strong pair domination number in VIG. Finally, an application of domination in illegal drug trade was introduced. Full article
(This article belongs to the Special Issue Fuzzy Graphs: Theory and Applications)
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24 pages, 1716 KiB  
Article
Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications
by Hao Guan, Waheed Ahmad Khan, Shazia Saleem, Waqar Arif, Jana Shafi and Aysha Khan
Axioms 2023, 12(12), 1120; https://doi.org/10.3390/axioms12121120 - 13 Dec 2023
Cited by 2 | Viewed by 1374
Abstract
Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity [...] Read more.
Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network. Full article
(This article belongs to the Special Issue Fuzzy Graphs: Theory and Applications)
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