The optimal group consensus deviation measure for multiplicative preference relations

Consistency and consensus measures are two important procedures employed in group decision making with multiplicative preference relations (MPRs). In this paper, we first establish the concept of individual consistency deviation degree between the original MPR and its optimal estimation. Then we develop a group consensus deviation degree optimization model (GCO Model) by minimizing the weighted arithmetic average of individual consistency deviation degrees. Our established theorems enlist the conditions for the existence of the optimal solution, the satisfactory solution, and non-inferior solution to the GCO Model. These results also provide an existence condition of redundant MPR in group decision making. Additionally, we show that the optimal value function of the GCO Model converges to 0, which implies that the consensus degree of DMs converges as the number of the decision makers increases indefinitely.

► We show the existing conditions of the optimal, satisfactory solutions to the GCO Model.
► We obtain the existence condition of the redundant GCO Model.
► We derive that the consensus either increases or stay invariant as the number of DM increases.