Operators and comparisons of probabilistic linguistic term sets

The probabilistic linguistic term sets (PLTSs) allow experts to express their preferences regarding one linguistic term over another. Nowadays, multicriteria decision-making methods for PLTSs are very popular, and Bai et al's multicriteria decision-making method based on the possibility degree formula for PLTSs cannot be ranked in some situations. In this paper, we first propose a new possibility degree method for PLTSs and state their properties, and we use this new possibility degree method to solve the drawbacks of Bai et al's possibility degree method. Second, we propose a probabilistic linguistic weight average (PLWA) and probabilistic linguistic order weight average (PLOWA) operator and state their properties. Then, based on the new possibility degree method and the PLWA (PLOWA) operator, we propose a multicriteria decision-making method based the PLWA (PLOWA) operator. Finally, we utilize an example to illustrate the interrelationships between our method and Bai et al's method. The result shows that our multicriteria decision-making method is more rational.