Bidirectional Projection Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Power Average Operator

The probabilistic linguistic terms set (PLTS) consists of several possible linguistic terms and their relative probability, and the Power average (PA) operator takes the interrelationships among the attributes into consideration. At the same time, the bidirectional projection (BP) method can consider the distance and the angle of the evaluated alternatives, moreover, it can also take the bidirectional projection magnitude into account. For the sake of fully taking the advantages of PLTS, PA operator and the BP method, in this article, we combine the PA operator with the BP method and extend it to the environment of probabilistic linguistic information (PLI), meanwhile, based on the calculation process of the weighted averaging operator of distribution assessments, the probabilistic linguistic PA (PLPA) operator and the weighted probabilistic linguistic PA (WPLPA) operator are proposed. Simultaneously, we discuss some properties of these operators. Further, we define the BP measures based on PLTS. Based on the combination of the WPLPA operator and the BP method, we develop the approach which can solve the problems of multiple attribute group decision-making with PLI. Lastly, a numerical instance is given to demonstrate the feasibility and the superiority of the proposed method.