Multi-criteria group decision making with preference approval structures: A personalized individual semantics approach

Some practical decision making problems need complex preferences. This study deals with a multi-criteria group decision making problem with preference approval structures (PASs). Each decision maker provides multi-criteria assessments in the form of linguistic distributions and a PAS of the alternatives. To ensure that the alternatives' scores computed from the multi-criteria assessments violate the ranking and approval information in the PAS to the least extent, an optimization model is constructed, and the minimum violation value is obtained. The maximum personalized individual semantics (PISs) and the minimum PISs of linguistic terms corresponding to the minimum violation value are obtained. By using the maximum and the minimum PISs of the linguistic terms, the ranking of the alternatives' scores is obtained. The approval information of the alternatives is obtained from an optimization model. Based on the ranking and approval information of the alternatives, two sequences of PASs corresponding to the maximum and the minimum PISs are obtained. An optimization model is proposed to fuse individual PASs into a collective PAS. A multi-criteria group decision making model is then proposed and applied in an example. Finally a comprehensive comparison analysis is presented to show the feasibility of the model.