A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Probabilistic linguistic term sets (PLTSs) are an effective tool for expressing subjective human cognition that offer advantages in the field of multi-attribute decision-making (MADM). However, studies have found that PLTSs have lost their ability to accurately capture the views of decision-makers (DMs) in certain circumstances, such as when the DM hesitates between multiple linguistic terms or the decision information is incomplete, thus affecting their role in the decision-making process. Belief function theory is a leading stream of thought in uncertainty processing that is suitable for dealing with the limitations of PLTS. Therefore, the purpose of this study is to extend PLTS to incorporate belief function theory. First, we provide the basic concepts of the extended PLTS (i.e., belief-based PLTS) through case analyses. Second, the aggregation operator of belief-based PLTS is defined with the ordered weighted average (OWA)-based soft likelihood function, which is improved by considering the reliability of the information source. Third, to measure the magnitude of different belief-based PLTSs, the belief interval of singleton is calculated, and the comparison method of belief-based PLTS is constructed based on probabilities. On the basis of the preceding discussion, we further develop an emergency decision framework that includes several novel techniques, such as attribute weight determination and decision information aggregation. Finally, the usefulness of the framework is demonstrated through a case study, and its effectiveness is illustrated through a series of comparisons.