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Multi-criteria social network group decision making (SNGDM) that allows decision makers (DMs) to interact with each other has attracted increasing attention in the field of decision analysis. In this paper, we take stochastic multicriteria acceptability analysis (SMAA) into account to study consensus reaching processes in multi-criteria SNGDM problems with manipulative behaviors. First, we propose a SMAA-based method to transform decision matrices into fuzzy preference relations to detect manipulators in multi-criteria SNGDM. Then, we design a new consensus determining mechanism using the weight stability interval and SMAA methods, which does not require a consensus threshold to be determined in advance. Based on this, we propose a two-stage feedback process to help DMs reach consensus. Then, we propose an algorithm to summarize the main steps of the proposed method. Finally, we use a case …