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The ranking of decision makers (DMs)’ preferences for feasible states in the graph model for conflict resolution (GMCR) is crucial for accurately determining stability results. This paper addresses the issue of subjective ranking methods lacking theoretical foundation and causing ambiguity when the number of feasible states is high by proposing the implementation of the multi-attribute decision-making (MADM) method in the GMCR. The paper utilizes the average level to choose evaluation based on distance from average solution (EDAS) method for determining the DM’s preference ranking, which can effectively reduce the impact of anomalous evaluations. Further, the PUL-EDAS method based on probabilistic uncertainty linguistics (PUL) is developed, which overcomes the shortcomings of the traditional EDAS method, which only applies to the simple evaluation of information. The PUL aligns with DMs’ daily …