Most scholars have established conflict analysis models based on the situation tables. Generally, agents tend to have imprecise assessments of issues, and their interpretations of issues are difficult to maintain consistency. The preference-based conflict analysis model aims to address these shortcomings, by employing ordered pairs over issues to replace three-value ratings in order to characterize conflict degree. However, the three-way conflict analysis models based on three-level preferences are insufficient to characterize preferences of agents. In this paper, we first define five preference relations and conflict situations based on these preference relations. Next, we assign conflict degrees to twenty-five different cases and define a conflict function for subsets of issues. Subsequently, we normalize the conflict degrees for subsets of issues and trisect the set of all pairs of agents. Finally, we validate the practicality of the model through examples. The proposed model guarantees more coherent data collection, simultaneously enhancing the explainability of preferences in three-way conflict analysis.