Intuitionistic 2-tuple linguistic aggregation information based on Einstein operations and their applications in group decision making

The linguistic information can be expressed as a 2-tuple of a linguistic variable and a real number in an interval [-12,12)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-\frac{1}{2}, \frac{1}{2})$$\end{document}. The intuitionistic 2-tuple linguistic (I2TL) set accurately deals with the imprecise and unpredictable information in those decision-making problems where experts prefer the degree of membership and non-membership values in the form of 2-tuple. The existing approaches used for the aggregation operations of I2TL sets are extremely complicated. This work aims to develop new aggregation operations for I2TL sets using Einstein operations. We present intuitionistic 2-tuple linguistic Einstein weighted averaging (I2TLEWA), and intuitionistic 2-tuple linguistic Einstein weighted geometric (I2TLEWG) operators. We also discuss their properties and relationship between them. Moreover, we numerically test the feasibility and significance of our proposed operators by solving a multi-criteria group decision making (MCGDM) problem. Finally, we do a comparative analysis with another method to give insights on our designed operators for I2TL sets.