Affiliations: [a] Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| [b] Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla, Thailand
Correspondence:
[*]
Corresponding author. Thammarat Panityakul, Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. E-mail: thammarat.p@psu.ac.th.
Abstract: In the real decision process, an important problem is how to express the attribute value more efficiently and accurately. In the real world, because of the complexity of decision-making problems and the fuzziness of decision-making environments, it is not enough to express attribute values of alternatives by exact values. For this managing with such sorts of issues, the principle of Linear Diophantine uncertain linguistic set is a valuable and capable technique to manage awkward and inconsistent information in everyday life problems. In this manuscript, we propose the original idea of Linear Diophantine uncertain linguistic set and elaborated their essential laws. Additionally, to determine the association among any numbers of attributes, we elaborated the Linear Diophantine uncertain linguistic arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic weighted arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic geometric Heronian mean operator, Linear Diophantine uncertain linguistic weighted geometric Heronian mean operator, and their properties are also discovered. By using these operators, we utilize the multi-attribute decision-making procedure by using elaborated operators. To determine the consistency and validity of the elaborated operators, we illustrate some examples by using explored operators. Finally, the superiority and comparative analysis of the elaborated operators with some existing operators are also determined and justified with the help of a graphical point of view.
Keywords: Linear Diophantine uncertain linguisticsets, arithmetic/geometric Heronian mean operators, decision-making methods
