<p>To better investigate the conflict problems of multiple decision makers with complex preferences, a new preference structure integrating interval grey preference, multi-level strength preference, and unknown preference is proposed within the framework of graph model for conflict resolution. The new preference structure is defined mathematically and different from the traditional logical preference expressions. The interval grey Nash stability, interval grey general metarationality stability, interval grey symmetric metarationality stability, interval grey sequential stability, and interval grey symmetric sequential stability are defined as four categories (a, b, c, and d) of general stabilities, strong stabilities, and weak stabilities to enable the equilibrium calculation under the new preference structure. Moreover, the graph model with the interval grey unknown and strength preference is applied to study a conflict of parts procurement under the background of Sino-US trade friction, considering the dual risk of supply chain disruption and product quality. Specifically, a graph model involving manufacturers, high-quality suppliers, and general suppliers is constructed to analyze the manufacturers’ procurement decision and the suppliers’ pricing strategy when the manufacturers adopt the dual source procurement option. The analysis results show that the proposed graph model with the new preference structure constitutes a suitable way to model the real-world conflicts and provide strategic suggestions for decision makers.</p>