Comparisons of probabilistic linguistic term sets for multi-criteria decision making

The theory of probabilistic linguistic term sets (PLTSs) is very useful in dealing with the multi-criteria decision making (MCDM) problems in which there is hesitancy in providing linguistic assessments; and PLTSs allow experts to express their preferences on one linguistic term over another. The existing approaches associated with PLTSs are limited or highly complex in real applications. Hence, the main purpose of this paper is to establish more appropriate comparison method and develop a more efficient way to handle with MCDM problems. We first put forward a diagram method to analyze the structures of PLTSs and develop the visualized way for readers to comprehend. Then a possibility degree formula is given for ranking PLTSs. Based on the new comparison method and the theory of the fuzzy preference relation, an efficient decision-making framework is proposed to solve real-life problems under linguistic environment. Conventional TOPSIS methods combined with PLTSs are also included for comparison. All results demonstrate the practicality of the new framework. Finally, we also seek out relationship between PLTSs and hesitant fuzzy linguistic term sets (HFLTSs), and compare the new formula with the similar approaches to HFLTSs' rating.