Integer Programming Models to Manage Consensus for Uncertain MCGDM Based on PSO Algorithms

In existing consensus models with optimization approaches, the modified preferences are often virtual values unrelated to the original rating scale. Furthermore, few optimization approaches have been developed to specifically deal with the consensus reaching process in uncertain multiple-criteria group decision making (MCGDM) problems. To investigate these issues, this paper is primarily interested in MCGDM optimization consensus models, in which the uncertain information can be represented using interval numbers. Integer optimization consensus models are established based on both the Manhattan distance and the Euclidean distance, and an antithetic-method-based particle swarm optimization algorithm is used to solve the nonlinear integer programming problems. Compared to existing approaches, the main characteristic of the proposed consensus models is that the generated preferences all belong to the original scales. A numerical example is given to validate the proposed models, and further simulation analyses shed light on the behavior of the developed models.