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• A self-organized mechanism based consensus framework is presented. • Non-cooperative behaviors are detected and managed at the element level of MAEMs. • A novel distance-based ordinal consensus measurement is proposed. • Simulation analysis is presented to show the effectiveness of our proposals. In consensus-based multi-attribute group decision making (MAGDM) problems, decision makers (DMs) may exhibit non-cooperative behaviors since they usually have different individual interests (sometimes conflicting) or limited knowledge, which strongly affects the efficiency of consensus and the quality of decision outcomes. Additionally, the existing MAGDM studies mainly focus on the cardinal consensus, and the ordinal consensus is ignored. Thus, this paper proposes a self-organized mechanism based framework to manage non-cooperative behaviors and ordinal consensus in MAGDM. First, a dual-membership function based on the basic idea of synergy theory is designed to detect non-cooperative behaviors at the element level of the multiple attribute evaluation matrix (MAEM), and then the weights of elements with non-cooperative behaviors are penalized automatically. In this way, the negative effects of non-cooperative behaviors can be eliminated. Next, a novel preference ranking-based ordinal consensus approach is proposed, which calculates an ordinal consensus based on the preference rankings of alternatives between individuals and the group. If the pre-defined consensus level is not reached, the feedback adjustment is used to help DMs modify their MAEMs to improve the consensus level; otherwise, the selection process is utilized to choose the optimal alternative(s). Finally, detailed simulation experiments and comparative analysis are designed to show the properties and effectiveness of the proposed framework, and an illustrative angel investment case is presented to demonstrate the calculation process and usability. [ABSTRACT FROM AUTHOR]