A Novel Probabilistic Linguistic Approach for Large-Scale Group Decision Making with Incomplete Weight Information

The large-scale group decision-making (GDM) problems with linguistic information have received more and more attentions; however, how to effectively manage the linguistic assessments provided by the large number of experts is still a challenge. In this paper, we employ the probabilistic linguistic term sets (PLTSs), which are the extension form of hesitant fuzzy linguistic term sets, to manage the large number of linguistic assessments. We also present a probabilistic linguistic distance measure for PLTSs. To address the large-scale probabilistic linguistic GDM problems in which the weights of groups are completely unknown or partially known in advance, we develop a probabilistic linguistic GDM method. First, we propose a consistency- and consensus-based model to objectively determine the weights of the groups. Then, to aggregate the opinions of all the groups, we propose a new probabilistic linguistic weighted arithmetic averaging operator and by using it the collective assessment of each alternative is obtained. Finally, the ranking of all alternatives is obtained on the basis of the dominance degrees and the optimal alternative is selected.