A method for group decision-making based on multi-granularity uncertain linguistic information

The multi-granularity uncertain linguistic term is a form of uncertain preference information in group decision-making (GDM), while it is seldom discussed in the existing research. In this paper, a method is proposed to solve the GDM problem with multi-granularity uncertain linguistic information. Firstly, to process multi-granularity uncertain linguistic information, a formula for transforming multi-granularity uncertain linguistic terms into trapezoidal fuzzy numbers is given based on the theoretical analysis. Thus, the GDM problem with multi-granularity uncertain linguistic information is changed into the one with fuzzy numbers. Then, to solve the GDM problem, an appropriate extension of the classical TOPSIS is conducted. Fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) are defined, respectively. The closeness coefficient is obtained to determine the ranking order of all alternatives by calculating the distances to both FPIS and FNIS, simultaneously. Finally, a numerical example is given to illustrate the use of the proposed method.