A method for multi-criteria decision making with probabilistic linguistic term based on cloud TOPSIS.

Recent literature has explored various approaches to address the stochasticity and ambiguity inherent in concept terms within the Multi-Criteria Decision Making (MCDM) process. Probabilistic linguistic terms provide a robust means to represent decision makers’ assessment preferences, such as the cloud model, which can describe the relationship between ambiguity and stochasticity using numerical characteristics. To ensure the accuracy and reliability of the decision making process, it is essential to integrate both implicit uncertainty and ambiguity information, which are often present. This study develops an MCDM technique to solve decision problems in which the criterion values are expressed as probabilistic linguistic terms. First, the cloud model is introduced, along with the concept of the probabilistic linguistic cloud. A golden section technique is employed to transform probabilistic linguistic terms into probabilistic linguistic clouds. Next, a novel distance metric between probabilistic linguistic clouds is presented, and a new cloud-weighted averaging operator (PLC-WA) is proposed to aggregate multiple probabilistic linguistic clouds. Subsequently, a new probabilistic linguistic cloud-TOPSIS (PLC-TOPSIS) method is introduced, and an MCDM approach based on PLC-TOPSIS is developed. Finally, a case study on group decision making for public evacuation during nuclear accidents is presented to validate the proposed method. The feasibility of the proposed method is verified through comparative analysis.