In real life, multiple network public opinion emergencies may break out in a certain place at the same time. So, it is necessary to invite emergency decision experts in multiple fields for timely evaluating the comprehensive crisis of the online public opinion, and then limited emergency resources can be utilized to give priority to respond to the one with the highest crisis. Due to the complexity of network public opinion emergencies and the limited cognition of experts, most of the decision (...) problems for evaluating the network public opinion emergencies are highly uncertain. Also, prior to the selection of the highest crisis, it is preferable that experts reach a high degree of consensus among their assessments or opinions. To address such problems, this paper presents a novel adaptive consensus reaching model for multiattribute group decision making with probabilistic linguistic decision matrices. First, to quantify the difference between any two probabilistic linguistic term sets accurately and efficiently, we define a novel distance measure between PLTSs based on the Wasserstein metric. Then, by integrating the defined PLTSs-based Wasserstein distance measure into the classical CCSD method, we construct an optimization model for objectively determining attribute weights. Subsequently, we develop the individual cumulative consensus contribution measure and the group consensus measure, respectively, following which is to present an integrated consensus improving strategy that considers both weight-updating and assessment-adjusting. Finally, the feasibility and the applicability of the proposed approach are illustrated via a real evaluation of network public opinion emergencies. Through comparing with existing probabilistic linguistic MAGDM approaches, the proposed approach offers the advantages in terms of the accurate measurement of information difference and the integrated improvement of consensus efficiency. (shrink)