A novel distance measure for probabilistic linguistic term sets with application to emergency decision-making

Probabilistic linguistic term sets (PLTSs), a form of fuzzy language, are capable of effectively expressing the evaluation information of decision-makers (DMs) in emergency decision-making (EDM) for disasters. Thus, an EDM method based on PLTSs and regret theory is proposed, addressing the uncertainty of decision-making information and the incomplete rationality of DMs in disaster scenarios. First, a novel distance measure method for PLTSs is established, integrating Euclidean distance, Jensen–Shannon (JS) divergence and Jousselme distance. Next, expert weights are determined based on the trust in each expert and the similarity of viewpoints. During consensus reaching, a feedback adjustment coefficient is introduced to maintain the integrity of the original evaluation information provided by the experts. Furthermore, a combined weighting method is developed, incorporating both objective and subjective attribute weights to derive comprehensive attribute weights. Taking into account the incomplete rationality of DMs, an EDM method is formulated using PLTSs and regret theory to prioritize alternatives. Finally, the effectiveness of the proposed method is validated through a case study using the selection of a transportation plan for relief supplies during the Yushu earthquake as an example, along with sensitivity analysis and a comparison with other existing approaches.