Aiming at the multicriteria group decisionmaking problem with unknown criteria weights, a new decision making method is proposed based on the priority obtained from the stochastic advantages, under the environment of Probabilistic Uncertain Linguistic Term Sets(PULTS), by determining the criteria weights through sufficiently considering decisionmakers’ evaluation on the importance between each criterion on the basis of individual preference, based on consistent criterion, and after comprehensively considering the hesitant degree when the experts make decision and the information in the evaluation made by the experts, which reduce the information loss in the process of decision making to some extent. Firstly, under PULTS environment, the uncertainty and score function are defined, the transformation from the linguistic set to number is realized, the expert weights are determined by using score function, and the comprehensive score matrix is further obtained. Secondly, the definition rule of stochastic advantages is applied to the definition of the priority of probabilistic uncertain linguistic set, and the weight of each criterion is determined according to the priority of each criterion. Finally, the related improvement is conducted on the basis of the consistent criterion decisionmaking law and is applied to PULTS environment. The feasibility and effectiveness of the new decisionmaking method are verified by numerical examples.