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

Zeeshan Ali, Tahir Mahmood and Gustavo Santos-García
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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

Mathematics, 2021, vol. 9, issue 21, 1-37

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.

Keywords: complex linear Diophantine uncertain linguistic sets; powered Einstein aggregation operators; multi-attribute decision-making methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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