Robust maximum expert consensus modeling with dynamic feedback mechanism under uncertain environments

The maximum expert consensus model (MECM) is an important decision method in group decision making (GDM). In previous research, decision makers' (DMs) soft consensus thresholds are often predetermined and fixed in MECM, leading to decreased effectiveness in achieving consensus. Therefore, we propose flexible MECMs with dynamic feedback adjustment mechanisms (DFA-MECMs) to guides DMs to modify consensus thresholds in CRP. However, dynamic adjustments of consensus thresholds in a real-world decision environment may lead to uncertainties in unit opinion adjustment costs. Moreover, DMs have different risk preferences on this uncertainty. To solve this problem, we employ robust optimization methods to construct three robust DFA-MECMs with different degrees of conservatism. Additionally, we develop a reference budget model to obtain a feasible budget range of robust DFA-MECMs. Furthermore, the effectiveness and superiority of robust DFA-MECMs are demonstrated using the consensus-achieving example of the carbon emission standard. Finally, sensitivity analysis and comparison analysis are presented and discussed.