A Visual Comparison Method and Similarity Measure for Probabilistic Linguistic Term Sets and Their Applications in Multi-criteria Decision Making

The probabilistic linguistic term sets (PLTSs) are very powerful in solving the multi-criteria decision-making (MCDM) problems. The previous comparison methods associated with PLTSs are finite and unreasonable. Hence, developing a more effective way to compare PLTSs and proposing a reasonable decision-making method to cope with MCDM problems are important work of this paper. Firstly, a new possibility degree is proposed and a visual comparison method is given to present the process of comparing PLTSs. Subsequently, a similarity measure for PLTSs is also proposed to make up for the lack of similarity measure. Combining the new comparison method with the similarity measure, the TOPSIS is extended to solve real-life problems under probabilistic linguistic environment. Finally, a numerical example considers the selection of public opinion monitoring systems and the comparative analyses are shown to illustrate the effectiveness of the proposed method.