Journal of Neutrosophic and Fuzzy Systems

Journal DOI

https://doi.org/10.54216/JNFS

Submit Your Paper

2771-6449ISSN (Online) 2771-6430ISSN (Print)

Volume 10 , Issue 1 , PP: 01-13, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

HyperFuzzy Graph and Hyperfuzzy HyperGraph

Takaaki Fujita 1 * , Prem Kumar Singh 2

  • 1 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan - (takaaki.fujita060@gmail.com)
  • 2 Department of Computer Science and Engineering, Gandhi Institute of Technology and Management, Visakhapatnam, Andhra Pradesh 530045, India - (premsingh.csjm@gmail.com)
  • Doi: https://doi.org/10.54216/JNFS.100101

    Received November 20, 2024, Revised December 24, 2024 Accepted January 14,2025
    Abstract

    Fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, plithogenic sets, and other uncertainty handling frameworks are the subject of intensive daily research. Analogous investigations have been pursued in the contexts of graphs, hypergraphs, and superhypergraphs. In this paper, we introduce new definitions of the hyperfuzzy hypergraph and superhyperfuzzy hypergraph, which extend the notion of the fuzzy hypergraph. We also revisit and refine the concepts of the hyperfuzzy graph and the superhyperfuzzy graph.

    Keywords :

    Hyperfuzzy set , Fuzzy set , SuperHyperfuzzy Set , Hyperfuzzy graph , Fuzzy graph , SuperHyper-fuzzy grap

    References

    [1] Muhammad Akram and Wieslaw A Dudek. Intuitionistic fuzzy hypergraphs with applications. Information Sciences, 218:182–193, 2013.

    [2] Mohammed Alshikho, Maissam Jdid, and Said Broumi. Artificial intelligence and neutrosophic machine learning in the diagnosis and detection of covid 19. Journal Prospects for Applied Mathematics and Data Analysis, 1(2), 2023.

    [3] Sk Amanathulla, Biswajit Bera, and Madhumangal Pal. Balanced picture fuzzy graph with application. Artificial Intelligence Review, 54(7):5255–5281, 2021.

    [4] Krassimir T Atanassov and Krassimir T Atanassov. Intuitionistic fuzzy sets. Springer, 1999.

    [5] Claude Berge. Hypergraphs: combinatorics of finite sets, volume 45. Elsevier, 1984.

    [6] Leonid S Bershtein and Alexander V Bozhenyuk. Fuzzy graphs and fuzzy hypergraphs. In Encyclopedia of Artificial Intelligence, pages 704–709. IGI Global, 2009.

    [7] Alain Bretto. Hypergraph theory. An introduction. Mathematical Engineering. Cham: Springer, 1, 2013.

    [8] Mahdi Farshi and Bijan Davvaz. Generalized fuzzy hypergraphs and hypergroupoids. Filomat, 30(9):2375–2387, 2016.

    [9] Yifan Feng, Haoxuan You, Zizhao Zhang, Rongrong Ji, and Yue Gao. Hypergraph neural networks. In Proceedings of the AAAI conference on artificial intelligence, volume 33, pages 3558–3565, 2019.

    [10] Takaaki Fujita. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutro- sophic, Soft, Rough, and Beyond. Biblio Publishing, 2025.

    [11] Jayanta Ghosh and Tapas Kumar Samanta. Hyperfuzzy sets and hyperfuzzy group. Int. J. Adv. Sci. Technol, 41:27–37, 2012.

    [12] Jonathan L Gross, Jay Yellen, and Mark Anderson. Graph theory and its applications. Chapman and Hall/CRC, 2018.

    [13] Mohammad Hamidi, Florentin Smarandache, and Mohadeseh Taghinezhad. Decision Making Based on Valued Fuzzy Superhyper- graphs. Infinite Study, 2023.

    [14] Young Bae Jun, Kul Hur, and Kyoung Ja Lee. Hyperfuzzy subalgebras of bck/bci-algebras. Annals of Fuzzy Mathematics and Informatics, 2017.

    [15] Waheed Ahmad Khan, Waqar Arif, Hossein Rashmanlou, and Saeed Kosari. Interval-valued picture fuzzy hypergraphs with appli- cation towards decision making. Journal of Applied Mathematics and Computing, 70(2):1103–1125, 2024.

    [16] Xiaowei Liao, Yong Xu, and Haibin Ling. Hypergraph neural networks for hypergraph matching. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1266–1275, 2021.

    [17] Muhammad Aslam Malik, Ali Hassan, Said Broumi, Assia Bakali, Mohamed Talea, and Florentin Smarandache. Isomorphism of bipolar single valued neutrosophic hypergraphs. Collected Papers. Volume IX: On Neutrosophic Theory and Its Applications in Algebra, page 72, 2022.

    [18] Berrocal Villegas Salom´on Marcos, Montalvo Fritas Willner, Berrocal Villegas Carmen Rosa, Flores Fuentes Rivera Mar´ıa Yissel, Espejo Rivera Roberto, Laura Daysi Bautista Puma, and Dante Manuel Macazana Fern´andez. Using plithogenic n-superhypergraphs to assess the degree of relationship between information skills and digital competencies. Neutrosophic Sets and Systems, 84:513– 524, 2025.

    [19] Nivetha Martin and Florentin Smarandache. Concentric plithogenic hypergraph based on plithogenic hypersoft sets–A novel outlook. Infinite Study, 2020.

    [20] Hossein Rashmanlou, Sovan Samanta, Madhumangal Pal, and Rajab Ali Borzooei. Intuitionistic fuzzy graphs with categorical properties. Fuzzy information and Engineering, 7(3):317–334, 2015.

    [21] Azriel Rosenfeld. Fuzzy graphs. In Fuzzy sets and their applications to cognitive and decision processes, pages 77–95. Elsevier, 1975.

    [22] Sovan Samanta and Madhumangal Pal. Bipolar fuzzy hypergraphs. International Journal of Fuzzy Logic Systems, 2(1):17–28, 2012.

    [23] Xiaolong Shi, Saeed Kosari, Hossein Rashmanlou, Said Broumi, and S Satham Hussain. Properties of interval-valued quadriparti- tioned neutrosophic graphs with real-life application. Journal of Intelligent & Fuzzy Systems, 44(5):7683–7697, 2023.

    [24] Muhammad Shoaib, Waqas Mahmood, Weded E Albalawi, and Faria Ahmad Shami. Notion of complex spherical fuzzy graph with application. Journal of Function Spaces, 2022.

    [25] Prem Kumar Singh et al. Dark data analysis using intuitionistic plithogenic graphs. International Journal of Neutrosophic Sciences, 16(2):80–100, 2021.

    [26] S Sivasankar and Said Broumi. Balanced neutrosophic graphs. Neutrosophic Sets and Systems, 50:309–319, 2022.

    [27] Florentin Smarandache. Hyperuncertain, superuncertain, and superhyperuncertain sets/logics/probabilities/statistics. Infinite Study, 2017.

    [28] Vicenc¸ Torra. Hesitant fuzzy sets. International journal of intelligent systems, 25(6):529–539, 2010.

     

    [29] Lotfi A Zadeh. Fuzzy sets. Information and control, 8(3):338–353, 1965.

    Cite This Article As :
    Fujita, Takaaki. , Kumar, Prem. HyperFuzzy Graph and Hyperfuzzy HyperGraph. Journal of Neutrosophic and Fuzzy Systems, vol. , no. , 2025, pp. 01-13. DOI: https://doi.org/10.54216/JNFS.100101
    Fujita, T. Kumar, P. (2025). HyperFuzzy Graph and Hyperfuzzy HyperGraph. Journal of Neutrosophic and Fuzzy Systems, (), 01-13. DOI: https://doi.org/10.54216/JNFS.100101
    Fujita, Takaaki. Kumar, Prem. HyperFuzzy Graph and Hyperfuzzy HyperGraph. Journal of Neutrosophic and Fuzzy Systems , no. (2025): 01-13. DOI: https://doi.org/10.54216/JNFS.100101
    Fujita, T. , Kumar, P. (2025) . HyperFuzzy Graph and Hyperfuzzy HyperGraph. Journal of Neutrosophic and Fuzzy Systems , () , 01-13 . DOI: https://doi.org/10.54216/JNFS.100101
    Fujita T. , Kumar P. [2025]. HyperFuzzy Graph and Hyperfuzzy HyperGraph. Journal of Neutrosophic and Fuzzy Systems. (): 01-13. DOI: https://doi.org/10.54216/JNFS.100101
    Fujita, T. Kumar, P. "HyperFuzzy Graph and Hyperfuzzy HyperGraph," Journal of Neutrosophic and Fuzzy Systems, vol. , no. , pp. 01-13, 2025. DOI: https://doi.org/10.54216/JNFS.100101