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This study put forwards a novel consensus framework to manage the consensus and weights (i.e., weights of the experts and attributes) in iterative multiple-attribute group decision making (MAGDM) problem. In this consensus framework, an optimization-based consensus model is devised to support the process of preferences-modifying, which seeks to minimize the adjustment amounts (in the sense of Manhattan distance) between the original and adjusted preferences. Then, the other two optimization-based consensus models are constructed to support the weights-updating, in which the consensus level among experts can be further improved. A numerical example is provided to show the application of the proposed consensus framework, and a detailed comparison analysis is presented to verify the effectiveness of the proposed consensus framework.