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New Concepts of Picture Fuzzy Graphs with Application

Author

Listed:
  • Cen Zuo

    (Artificial Intelligence and Big Data College, Chongqing College of Electronic Engineering, Chongqing 401331, China)

  • Anita Pal

    (Department of Mathematics, National Institute of Technology, Durgapur 713209, India)

  • Arindam Dey

    (Department of Computer Science and Engineering, Saroj Mohan Institute of Technology, Hooghly 712512, India)

Abstract

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network.

Suggested Citation

  • Cen Zuo & Anita Pal & Arindam Dey, 2019. "New Concepts of Picture Fuzzy Graphs with Application," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:470-:d:234131
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    References listed on IDEAS

    as
    1. Zeshui Xu & Hui Hu, 2010. "Projection Models For Intuitionistic Fuzzy Multiple Attribute Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 267-280.
    2. Bhagawati P. Joshi & Sanjay Kumar, 2012. "Fuzzy Time Series Model Based on Intuitionistic Fuzzy Sets for Empirical Research in Stock Market," International Journal of Applied Evolutionary Computation (IJAEC), IGI Global, vol. 3(4), pages 71-84, October.
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