Interval-valued probabilistic linguistic term sets in multi-criteria group decision making

The theory of probabilistic linguistic term sets (PLTSs) is very useful in objectively dealing with the multi-criteria group decision making (MCGDM) problems in which there is hesitancy in providing linguistic assessments; and PLTSs allow experts to express their preferences on one linguistic term over another. In order to reflect the uncertainty and inconsistency of decision-makers and handle incomplete linguistic information, we propose a new PLTS called interval-valued probabilistic linguistic term set (IVPLTS). In addition, the existing approaches associated with PLTSs are limited or highly complex in real applications. Therefore, new operations, comparison laws, and aggregation operators are developed for IVPLTS. Furthermore, we establish an efficient framework for MCGDM problems based on the proposed comparison method and the fuzzy preference relation. Then we apply it to a real-life case under linguistic environment. The extended TOPSIS methods combined with PLTSs by using different operational laws are also included for comparison. The final results demonstrate the efficiency and practicality of the new framework.