A consensus-based method for group decision making with incomplete uncertain linguistic preference relations

In practical group decision-making (GDM) problems, it is nature for experts to express their preference relations in uncertain linguistic pattern, due to the ambiguity of the external environments and the internal nature of human judgments. In this paper, a consensus process is introduced to deal with GDM problems with incomplete uncertain linguistic preference relations (ULPRs). Firstly, a consistency level for ULPRs is defined. Secondly, a linear goal programming model is furnished to estimate the missing uncertain linguistic preference values with respect to consistency property. Thirdly, an additively consistent ULPR is constructed. What’s more, one can obtain the collective ULPR by aggregating individual additively consistent ULPRs, where the order-inducing variable is consistency level (CL), based on the thought of more importance will be given to the larger CL. Furthermore, a consensus reaching process is presented to make experts’ opinions achieve to a predefined level. In the end, a new algorithm is proposed to solve the GDM problem with incomplete ULPR, which is further applied to the selection of best cooperator in a water conservancy project.