Alternative ranking in trust network group decision-making: A distributionally robust optimization method

Abstract

In group decision making problems, preference information can be conveniently and productively used to express the decision-makers’ evaluations over the given set of alternatives. However, the inherent imprecision of preference information may lead to fragile priority weights and unreliable alternative ranking. In this study, we propose a distributionally robust ranking model based on social networks to derive stable priorities, which takes into account the influence of uncertain preference information and the strength of relationships among decision-makers. Specifically, to capture the true data-generating distribution of uncertain parameters, we first develop a distributionally robust ranking model with a moment-based ambiguity set that contains all possible probability distributions over a support set. Then, we verify that the solutions exhibit strong finite-sample performance guarantees. Additionally, the developed model can be reformulated into an equivalent semidefinite programming model. To account for the strength of relationships among decision-makers, we employ propagation efficiency based on Shannon’s theorem, and develop the trust propagation and aggregation operators to obtain decision-makers’ weights. Finally, a numerical experiment is provided, in which the justification and robustness of the distributionally robust ranking model outperform several benchmark models by comparative discussions and robustness analyses.