Minimum cost consensus modeling under dynamic feedback regulation mechanism considering consensus principle and tolerance level

Since the hard consensus is difficult and costly to achieve in group decision making (GDM), it is reasonable and necessary for decision makers (DMs) to reach a soft consensus within a certain level of tolerance and consensus. To achieve this purpose, the concepts and definitions of consensus principle, tolerance level and consensus level are proposed in this paper. The consensus principle keeps the consensus reaching process (CRP) always moving in a better direction, and the tolerance level characterizes the individual’s psychological receptivity, while the consensus level guarantees the quality of consensus results, then the minimum cost consensus models (MCCMs) based on these three points are proposed. Thereafter, we add a feedback regulation mechanism based on tolerance threshold rewards to the proposed MCCMs, the mechanism connects individual weight with tolerance threshold, avoiding the subjective disadvantage caused by the two values need to be given in advance. Meanwhile, the framework and specific algorithm of CRP under the tolerance threshold reward feedback regulation mechanism are given, providing a precise method for solving the realistic consensus problems. Finally, the consensus reaching case of the carbon emission benchmark shows the reasonable effectiveness of the two different models proposed in this paper, and the comparative analysis shows the differences and applicability of the two models.