Multicriteria decision-making methods and application on the basis of probabilistic uncertain trapezium cloud

Probabilistic Uncertain Linguistic Term Set (PULTS), as an emerging and effective linguistic expression tool, can appropriately describe the complex evaluation information of decision makers. The cloud model is powerful in handling complex cognitive linguistic information, based on which, this paper proposes two new Multicriteria Decision-Making (MCDM) Methods with PULTSs. Firstly, to avoid the problem of information loss in traditional linguistic conversion methods, Probabilistic Uncertainty Trapezium Cloud (PUTC) is proposed to quantify linguistic evaluation information. Secondly, the Probabilistic Uncertainty Trapezium Cloud Weighted Bonferroni mean (PUTCWBM) operator is defined, while presenting a new cloud score function and similarity measures. Additionally, two ranking methods are proposed, one on the basis of the similarity measures of PUTCs and ideal solutions, the other on the basis of the PUTCWBM operator and the cloud score function. Finally, the two methods are verified with an example of evaluation on masks, and the effectiveness and superiority of the methods are further illustrated through sensitivity analysis and method comparison.