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Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

Author

Listed:
  • Zeeshan Ali

    (Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan)

  • Tahir Mahmood

    (Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan)

  • Gustavo Santos-García

    (Instituto Multidisciplinar de Empresa (IME), University of Salamanca, 37007 Salamanca, Spain)

Abstract

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.

Suggested Citation

  • Zeeshan Ali & Tahir Mahmood & Gustavo Santos-García, 2021. "Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making," Mathematics, MDPI, vol. 9(21), pages 1-37, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2730-:d:666313
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    References listed on IDEAS

    as
    1. Tahir Mahmood & Ali Jaballah, 2020. "A Novel Approach towards Bipolar Soft Sets and Their Applications," Journal of Mathematics, Hindawi, vol. 2020, pages 1-11, October.
    2. Harish Garg, 2017. "Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process," Computational and Mathematical Organization Theory, Springer, vol. 23(4), pages 546-571, December.
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    Cited by:

    1. Anam Habib & Zareen A. Khan & Muhammad Riaz & Dragan Marinkovic, 2023. "Performance Evaluation of Healthcare Supply Chain in Industry 4.0 with Linear Diophantine Fuzzy Sine-Trigonometric Aggregation Operations," Mathematics, MDPI, vol. 11(12), pages 1-29, June.

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