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Energy of Pythagorean Fuzzy Graphs with Applications

Author

Listed:
  • Muhammad Akram

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

  • Sumera Naz

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

Abstract

Pythagorean fuzzy sets (PFSs), an extension of intuitionistic fuzzy sets (IFSs), inherit the duality property of IFSs and have a more powerful ability than IFSs to model the obscurity in practical decision-making problems. In this research study, we compute the energy and Laplacian energy of Pythagorean fuzzy graphs (PFGs) and Pythagorean fuzzy digraphs (PFDGs). Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of PFGs. Finally, we present numerical examples, including the design of a satellite communication system and the evaluation of the schemes of reservoir operation to illustrate the applications of our proposed concepts in decision making.

Suggested Citation

  • Muhammad Akram & Sumera Naz, 2018. "Energy of Pythagorean Fuzzy Graphs with Applications," Mathematics, MDPI, vol. 6(8), pages 1-27, August.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:8:p:136-:d:163098
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    References listed on IDEAS

    as
    1. Sunil Mathew & John N. Mordeson, 2017. "Fuzzy Incidence Blocks and their Applications in Illegal Migration Problems," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 245-260, November.
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