A novel graph model with time-varying altitudes is developed to interpret the trade disputes between China and the United States (US) during the period between 2017 and 2019. The implementation of strategies for China and the US was affected by their bilateral relations represented by mutual attitudes changing over time along the evolution of the disputes. The Goldstein scale, a numeral system for studying foreign policies and for describing the fluctuating diplomatic relations affected by historical events, is utilized for eliciting preference relations affected by the time-varying attitudes for the first time. By considering two decision makers (DMs) in the trade disputes, the time varying unilateral improvements (TVUIs) for each DM are initiated based on its judgement which reflects not only the gains or losses for the given DM, but also those for the other DM. In investigating the real-world trade disputes between China and the US, the reasoning of imposing retaliating tariffs for the two countries under time frame is explained. How the fluctuation of time-varying altitudes affects the course of the disputes is also demonstrated. The Phase one agreement legally prohibiting retaliation using tariffs from the two countries was signed when mutual attitude increased by positive interstate events, which eventually ended the tit-for-tat situation. This novel methodology extends the structure of attitudes in graph model by flexibly depicting the fluctuation of mutual attitudes using Goldstein scoring system. Meaningful implications can be provided for DMs to explain how equilibrium can be changed by the time-varying attitudes. In analyzing international disputes in particular, nations can be clearly guided to achieve desired outcomes by making efforts to change bilateral or multilateral relations.