Some proportional 2-tuple geometric aggregation operators for linguistic decision making

In this paper, we investigate decision making problems with fuzzy linguistic information. Motivated by the idea of proportional 2-tuple PT, we develop some new aggregation operators such as PT weighted geometric averaging operator, PT ordered weighted geometric averaging operator and PT hybrid geometric averaging operator, which can be utilized to aggregate preference information taking the form of linguistic variables, and study some desirable properties. Based on the aforesaid operators, we develop a practical method for decision making under the PT linguistic environments. Finally, an example is given to verify the developed approach and demonstrate its practicality and effectiveness.