Robust minimum cost consensus models with aggregation operators under individual opinion uncertainty

Abstract

Individual opinion is one of the vital factors influencing the consensus in group decision-making, and is often uncertain. The previous studies mostly used probability distribution, interval distribution or uncertainty distribution function to describe the uncertainty of individual opinions. However, this requires an accurate understanding of the individual opinions distribution, which is often difficult to satisfy in real life. In order to overcome this shortcoming, this paper uses a robust optimization method to construct three uncertain sets to better characterize the uncertainty of individual initial opinions. In addition, we used three different aggregation operators to obtain collective opinions instead of using fixed values. Furthermore, we applied the numerical simulations on flood disaster assessment in south China so as to evaluate the robustness of the solutions obtained by the robust consensus models that we proposed. The results showed that the proposed models are more robust than the previous models. Finally, the sensitivity analysis of uncertain parameters was discussed and compared, and the characteristics of the proposed models were revealed.

Distributionally Robust Two-Stage Minimum Asymmetric Adjustment Cost Consensus Model with Risk Aversion

“…In the robust optimization method, Han et al [25] considered the uncertainty in the input data and established the minimum cost consensus model based on the RO method with four different uncertainty sets. Wei et al [26] proposed three robust consensus models which used three different aggregation operators, and set novel Box ambiguous set, Ellipsoid ambiguous set, and Polyhedron ambiguous set to study. Jin et al [27] used the RO method to study the MADM problem and established mixed 0-1 robust optimization model.…”