On compatibility of uncertain additive linguistic preference relations and its application in the group decision making

We develop a new compatibility for the uncertain additive linguistic preference relations and utilize it to determine the optimal weights of experts in the group decision making (GDM). Based on some operational laws for the uncertain additive linguistic preference labels, we propose some new concepts of the compatibility degree and acceptable compatibility index for the two uncertain additive linguistic preference relations. We also prove the properties that the synthetic preference relation is also of acceptable compatibility under the condition that additive linguistic preference relations provided by experts are all of acceptable compatibility with the specific linguistic preference relation, which provides a theoretic basis for the application of the uncertain additive linguistic preference relations in the GDM. Furthermore, we establish a mathematical model to obtain the weights of experts based on the criterion of minimizing the compatibility in the GDM, and we discuss the solution to the model. Finally, we give a numerical example to make comparative analysis on compatibility index using the optimal experts’ weights approach and the equal experts’ weights approach, which indicates that the model is feasible and effective.