On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and utilize it to determine the optimal weights of experts in the group decision making (GDM). First, the compatibility degree and compatibility index for the two multiplicative linguistic preference relations are proposed. Then, based on the linguistic continuous ordered weighted geometric averaging (LCOWGA) operator, some concepts of the compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are presented. We prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that the uncertain multiplicative linguistic preference relations given by experts are all of acceptable compatibility with the ideal uncertain multiplicative linguistic preference relation, which provides a theoretic basis for the application of the uncertain multiplicative linguistic preference relations in GDM. Next, an optimal model is constructed to determine the weights of experts based on the criterion of minimizing the compatibility index in GDM. Moreover, an approach to GDM with uncertain multiplicative linguistic preference relations is developed, and finally, an application of the approach to supplier selection problem with uncertain multiplicative linguistic preference relations is pointed out.