A PSO-based group decision making model with multiplicative reciprocal matrices under flexibility

Using the method of the analytic hierarchy process (AHP), multiple experts are invited to pairwise compare a finite set of alternatives and find a solution in group decision making. Under the AHP framework, the given multiplicative reciprocal preference relations are allowed to be deviated from the consistent matrices to a certain degree. In this study, it is assumed that the initial positions of the experts in a group decision making problem are characterized by multiplicative reciprocal matrices over a set of alternatives. A flexibility degree is offered to each expert so that her/his position can be modified opportunely. The information granules are constructed according to two different approaches. In order to build consensus in group decision making, a novel objective function is established to measure the consensus level within the multiple experts and to quantify the level of group consistency. Based on a modified particle swarm optimization (PSO) algorithm, the dynamic and iterative consensus process in group decision making is modeled by minimizing the objective function. Numerical results are reported to illustrate the proposed consensus model in group decision making. The novelty is revealed by comparing the existing group decision making model based on the PSO method. The proposed model could be used to deal with the large-scale group decision making problem with social network information.