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Issue:Analysis of hub parameters in fuzzy hypergraphs extending to intuitionistic fuzzy threshold hypergraphs: Applications in designing transport networks in amusement parks using hub hyperpaths

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Title of paper: Analysis of hub parameters in fuzzy hypergraphs extending to intuitionistic fuzzy threshold hypergraphs: Applications in designing transport networks in amusement parks using hub hyperpaths
Author(s):
K. K. Myithili
Department of Mathematics (CA), Vellalar College for Women, Erode-638012, Tamilnadu, India
mathsmyth@gmail.com
C. Nandhini
Department of Mathematics (CA), Vellalar College for Women, Erode-638012, Tamilnadu, India
c.nandhini@vcw.ac.in
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 3, pages 242–259
DOI: https://doi.org/10.7546/nifs.2024.30.3.242-259
Download:  PDF (2406  Kb, File info)
Abstract: A hypergraph is a generalization of a graph where an edge can connect any number of vertices. In this paper, many different aspects of fuzzy hypergraphs and their applications are examined. The concepts of the hub hyperpath, hub set, and hub number of fuzzy hypergraphs are defined and analyzed. Specifically, the hub number in complete fuzzy hypergraphs has been analyzed and provided an example as an application part in transportation systems. Furthermore, these concepts have been expanded to Intuitionistic Fuzzy Hypergraphs (IFHGs), defining the hub hyperpath, hub set, and hub number. Additionally, the problem of designing an efficient electric transport system for moving between game stations in a large amusement park has been investigated using hub analysis within the framework of an Intuitionistic Fuzzy Threshold Hypergraph (IFTHG) environment.
Keywords: Hub analysis, Hub number of fuzzy hypergraph, Intuitionistic fuzzy hypergraph (IFHG), Intuitionistic fuzzy threshold hypergraphs (IFTHG), Transport network
AMS Classification: 05C65, 05C72.
References:
  1. Berge, C. (1989). Hypergraphs. Elsevier Science Publishers B.V., North-Holland Mathematical Library.
  2. Bretto, A. (2013). Hypergraph Theory. Springer International Publishing Switzerland.
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  4. Khalaf, S. I., Mathad, V., & Mahde, S. S. (2020). Hub and global hub numbers of a graph. Proceedings of the Jangjeon Mathematical Society, 23(2), 231–239.
  5. Myithili, K. K., & Nandhini, C. (2024). Hub parameters of hypergraph. Journal of the Indonesian Mathematical Society, 30(1), 100–109.
  6. Myithili, K. K., & Nandhini, C. (2024). Intuitionistic fuzzy threshold hypergraphs: Introduction and review. Futuristic Trends in Contemporary Mathematics & Applications, IIP Series, 3(1), 61–75.
  7. Parvathi, R., Thilagavathi, S., & Karunambigai, M. G. (2009). Intuitionistic fuzzy hypergraphs. Cybernetics and Information Technologies, 9(2), 46–53.
  8. Radhika, C., & Parvathi, R. (2016). Intuitionistic fuzzification functions. Global Journal of Pure and Applied Mathematics, 12(2), 1211–1227.
  9. Walsh, M. (2006). The hub number of a graph. International Journal of Mathematics and Computer Science, 1, 117–124.
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