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Fuzzy Coalition Graphs: A Framework for Understanding Cooperative Dominance in Uncertain Networks

Author

Listed:
  • Yongsheng Rao

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Srinath Ponnusamy

    (Department of Mathematicas, Sri Sivasubramaniya Nadar College of Engineering, Chennai 603110, India)

  • Sundareswaran Raman

    (Department of Mathematicas, Sri Sivasubramaniya Nadar College of Engineering, Chennai 603110, India)

  • Aysha Khan

    (Department of Mathematicss, University of Technology and Applied Sciences Musanna, Al-Musannah 314, Oman)

  • Jana Shafi

    (Department of Computer Engineering and Information, College of Engineering in Wadi Alddawasir, Prince Sattam Bin Abdulaziz University, Wadi Alddawasir 11991, Saudi Arabia)

Abstract

In a fuzzy graph G , a fuzzy coalition is formed by two disjoint vertex sets V 1 and V 2 , neither of which is a strongly dominating set, but the union V 1 ∪ V 2 forms a strongly dominating set. A fuzzy coalition partition of G is defined as Π = { V 1 , V 2 , ⋯ , V k } , where each set V i either forms a singleton strongly dominating set or is not a strongly dominating set but forms a fuzzy coalition with another non-strongly dominating set in Π . A fuzzy graph with such a fuzzy coalition partition Π is called a fuzzy coalition graph, denoted as FG ( G , Π ) . The vertex set of the fuzzy coalition graph consists of { V 1 , V 2 , ⋯ , V k } , corresponding one-to-one with the sets of Π , and the two vertices are adjacent in FG ( G , Π ) if and only if V i and V j are fuzzy coalition partners in Π . This study demonstrates how fuzzy coalition graphs can model and optimize cybersecurity collaborations across critical infrastructures in smart cities, ensuring comprehensive protection against cyber threats. This study concludes that fuzzy coalition graphs offer a robust framework for optimizing collaboration and decision-making in interconnected systems like smart cities.

Suggested Citation

  • Yongsheng Rao & Srinath Ponnusamy & Sundareswaran Raman & Aysha Khan & Jana Shafi, 2024. "Fuzzy Coalition Graphs: A Framework for Understanding Cooperative Dominance in Uncertain Networks," Mathematics, MDPI, vol. 12(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3614-:d:1524525
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