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Article

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

1
Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan
2
Instituto Multidisciplinar de Empresa (IME), University of Salamanca, 37007 Salamanca, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Antonio Francisco Roldán López de Hierro
Mathematics 2021, 9(21), 2730; https://doi.org/10.3390/math9212730
Received: 9 September 2021 / Revised: 23 September 2021 / Accepted: 12 October 2021 / Published: 27 October 2021
(This article belongs to the Special Issue Fuzzy Sets and Artificial Intelligence)
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. View Full-Text
Keywords: complex linear Diophantine uncertain linguistic sets; powered Einstein aggregation operators; multi-attribute decision-making methods complex linear Diophantine uncertain linguistic sets; powered Einstein aggregation operators; multi-attribute decision-making methods
MDPI and ACS Style

Ali, Z.; Mahmood, T.; Santos-García, G. Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making. Mathematics 2021, 9, 2730. https://doi.org/10.3390/math9212730

AMA Style

Ali Z, Mahmood T, Santos-García G. Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making. Mathematics. 2021; 9(21):2730. https://doi.org/10.3390/math9212730

Chicago/Turabian Style

Ali, Zeeshan, Tahir Mahmood, and 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 9, no. 21: 2730. https://doi.org/10.3390/math9212730

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