A projection method for multiple attribute group decision making with probabilistic linguistic term sets

In multiple attribute group decision making (MAGDM) processes, decision makers often use hesitant fuzzy linguistic term sets (HFLTSs) to express their opinions. However, it is incapable of representing the importance degrees or weights of different linguistic terms. The probabilistic linguistic term set (PLTS) gives each linguistic term a probability to denote their importance degree, and thus is more suitable for group decision making problems where the distribution information is available. In this paper, the PLTSs are utilized to express the experts' assessments on each alternative with respect to each attribute in the MAGDM problem. Additionally, we establish two optimization models to derive the attribute weights. Then we propose a projection model to calculate the alternatives' projections on both the positive and negative ideal solutions. A practical decision making problem about crossover development is given to validate the effectiveness of the projection method with PLTS information. Finally, we make some comparisons between the projection method and other existing methods, meanwhile, the advantages and limitations of the projection model are summarized.