Externality may have uncertain influence on decision makers (DMs). To address the conflicts with uncertain preference and externality, this study adopts the general grey number to measure the uncertain value of DMs’ option statements influenced by externality. It constructs adjustable grey preference influenced by externality (GPE), which can be dynamically adjusted according to the influence of externality. Subsequently, the study defines four equilibrium solutions for the graph model for conflict resolution based on grey preference influenced by externality (GPE-GMCR). Finally, the method is applied to a commercial bank operating conflict triggered by the Silicon Valley Bank (SVB) collapse in the United States, resulting in optimal results for conflict resolution. Specifically, the new model provides a practical tool for DMs, managers and policy makers to address conflicts arising from DMs’ uncertain preference under the influence of externality in complex environments.

中文翻译：

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灰色偏好分析冲突解决图模型中外部性的影响

外部性可能对决策者（DM）产生不确定的影响。为了解决不确定性偏好与外部性的冲突，本研究采用一般灰数来衡量决策者期权陈述受外部性影响的不确定性价值。构建受外部性影响的可调节灰色偏好（GPE），可以根据外部性的影响进行动态调整。随后，研究定义了基于外部性影响的灰色偏好的冲突解决图模型（GPE-GMCR）的四种平衡解。最后将该方法应用于美国硅谷银行（SVB）倒闭引发的商业银行经营冲突中，得到了冲突解决的最优结果。具体来说，新模型为决策者、管理者和政策制定者提供了解决复杂环境下决策者在外部性影响下的不确定偏好所产生的冲突的实用工具。