We develop a new compatibility for the uncertain additive linguistic preference relations and study its properties which are very suitable to deal with group decision making (GDM) problems involving uncertain additive linguistic preference relations. Based on the linguistic continuous ordered weighted averaging (LCOWA) operator, we present some concepts of the compatibility degree and compatibility index for the two uncertain additive linguistic preference relations. Then, we study some desirable properties including the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain additive linguistic preference relations given by experts are all of acceptable compatibility with the ideal uncertain linguistic preference relation, which provides a theoretic basis for the application of the uncertain additive linguistic preference relations in GDM. In order to determine the weights of experts, we construct an optimal model based on the criterion of minimizing the compatibility index in GDM. Finally, we propose a new approach based on the compatibility index and the expected additive linguistic preference relation to GDM and develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the evaluation of schools in a university. 
On compatibility of uncertain additive linguistic preference relations based on the linguistic COWA operator