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Granulation of Hypernetwork Models under the q -Rung Picture Fuzzy Environment

Author

Listed:
  • Anam Luqman

    (Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan)

  • Muhammad Akram

    (Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan)

  • Ali N. A. Koam

    (Department of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan 45142, Saudi Arabia)

Abstract

In this paper, we define q -rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q -rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q -rung picture fuzzy equivalence relation and q -rung picture fuzzy hierarchical quotient space structures. In particular, a q -rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q -rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q -rung picture fuzzy hypergraphs and the q -rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

Suggested Citation

  • Anam Luqman & Muhammad Akram & Ali N. A. Koam, 2019. "Granulation of Hypernetwork Models under the q -Rung Picture Fuzzy Environment," Mathematics, MDPI, vol. 7(6), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:496-:d:236333
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    References listed on IDEAS

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    1. Muhammad Akram & Anam Luqman, 2017. "Intuitionistic single-valued neutrosophic hypergraphs," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 799-815, December.
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