A large-scale group decision-making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection

A large amount of stakeholders take part in the decision-making process, usually called a large-scale group decision-making (LGDM) problem. Some stakeholders may only provide partial preference information because of the limitation of knowledge over the alternatives. In this paper, a LGDM model is proposed to handle such problems, in which the incomplete multi-granular linguistic information showcases more appropriateness in respect of multi-stakeholders to represent their assessments. Meanwhile, the proposed model attains the maximum information from all decision makers and avoids an oversimplification for the elicited information in traditional linguistic models. It is more significant that we present three normalising methods for the purpose of securing the complete probabilistic linguistic term sets (PLTSs) based on risk attitudes: optimistic, pessimistic and neutral, respectively. In addition, alternatives are ranked by the extended TOPSIS method. Finally, a sustainable supplier selection is used to validate the effectiveness of the proposed model.