Multi-attribute decision making method based on generalized maclaurin symmetric mean aggregation operators for probabilistic linguistic information

Abstract The generalized Maclaurin symmetric mean (GMSM) operator not only can consider the interrelationship among the multi-input arguments, but also can be flexibly converted to many existing operators by adjusting the parameters. The probabilistic linguistic terms set (PLTS) can give different important degrees of all given evaluation values, and provide more accurate information for the decision making. In order to fully take the advantages of the GMSM operator and probabilistic linguistic information (PLI), in this paper, we extend the GMSM operator to PLI, and four new aggregated operators are proposed, including the probabilistic linguistic GMSM (PLGMSM) operator, the probabilistic linguistic geometric MSM (PLGeoMSM) operator, the weighted probabilistic linguistic GMSM (WPLGMSM) operator and the weighted probabilistic linguistic geometric MSM (WPLGeoMSM) operator. In the Meanwhile, we discuss their properties and special cases. Further, based on proposed WPLGMSM operator and the WPLGeoMSM operator, a novel approach for multi-attribute group decision making (MAGDM) problems with PLI is proposed. Finally, a numerical example is given to illustrate the feasibility and superiority of the proposed method.