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Randić energies for T-spherical fuzzy Hamacher graphs and their applications in decision making for business plans

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Abstract

To imitate the uncertainty and ambiguity in various decision-making problems, the T-spherical fuzzy set is more pragmatic and influential than the picture fuzzy set and q-rung orthopair fuzzy set. Because of the vagueness and fuzziness found in real-life problems, in which intuitionistic fuzzy sets may not give adequate results, the T-spherical fuzzy set is an efficient mathematical model to deal with them and can be handled effectively by using the notion of T-spherical fuzzy sets. In a different framework which is based on more opinions like yes, no, refusal, and abstaining, the T-spherical fuzzy set has been proven to be the most beneficial. In this article, we proposed the idea of T-spherical fuzzy Hamacher graphs (TSFHGs) based on Hamacher t-norm and t-conorm. We investigate the notion of the energy of TSFHGs, splitting TSFHGs, and shadow TSFHGs. Further, we introduce the Randić energy of TSFHG and studied its fundamental results. Moreover, we introduced the T-spherical fuzzy Hamacher digraphs (TSFHDGs) and discussed various results. We studied the applications of the proposed energies of TSFHGs in a decision-making problem by using an algorithm involving TSFHDGs and Hamacher aggregation operators. We also established a comparative study to see the significance of our proposed results.

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Acknowledgements

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R192), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, Riphah International University Lahore, Lahore, Pakistan

    Khushbakhat Asif, Muhammad Kamran Jamil, Muhammad Azeem & Kifayat Ullah

  2. Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O.Box 84428, Riyadh, 11671, Saudi Arabia

    Hanen Karamti

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  1. Khushbakhat Asif
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  2. Muhammad Kamran Jamil
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  3. Hanen Karamti
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  4. Muhammad Azeem
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  5. Kifayat Ullah
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Correspondence to Muhammad Azeem.

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Communicated by Graçaliz Pereira Dimuro.

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Asif, K., Jamil, M.K., Karamti, H. et al. Randić energies for T-spherical fuzzy Hamacher graphs and their applications in decision making for business plans. Comp. Appl. Math. 42, 106 (2023). https://doi.org/10.1007/s40314-023-02243-8

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  • DOI: https://doi.org/10.1007/s40314-023-02243-8

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