A multi-stage group decision making approach for sustainable supplier selection based on probabilistic linguistic time-ordered incentive operator

This study proposes a novel multi-stage multi-attribute group decision making method under a probabilistic linguistic environment considering the development state and trend of alternatives. First, the probabilistic linguistic term set (PLTS) is used by decision makers (DMs) to describe qualitative evaluation information. Subsequently, the weights of DMs for different attributes in different periods are determined by the credibility degree, which is combined with the hesitancy degree and the similarity degree. The evaluations of different DMs for alternatives and the evaluations of DMs’ intentions to reward or punish are then aggregated. Later, the trend change level and the trend change stability of alternatives are measured through the means of reward and punishment incentives. Additionally, the probabilistic linguistic time-ordered incentive operator is proposed to aggregate the development state evaluation information and development trend evaluation information in different periods, and alternatives are prioritized by the extended TOPSIS method in the probabilistic linguistic environment. Finally, the practical use of the proposed decision framework is validated by using a sustainable supplier selection problem, and the effectiveness and the applicability of the framework are discussed through comparative analysis. The results show that the proposed approach can select suitable sustainable suppliers by considering their development state and trend in multiple stages.