In three-way conflict analysis, preference-based conflict situations characterize agents' attitudes towards issues by formally modeling their preferences over pairs of issues. However, existing preference-based conflict models rely exclusively on three qualitative relations, namely, preference, converse, and indifference, to describe agents' attitudes towards issue pairs, which significantly limits their capacity in capturing the essence of conflict. To overcome this limitation, we introduce the concept of an intuitionistic fuzzy preference-based conflict situation that captures agents' attitudes towards issue pairs with finer granularity than that afforded by classical preference-based models. Afterwards, we develop intuitionistic fuzzy preference-based conflict measures within this framework, and construct three-way conflict analysis models for trisecting the set of agent pairs, the agent set, and the issue set. Additionally, relative loss functions built on the proposed conflict functions are employed to calculate thresholds for three-way conflict analysis. Finally, we present adjustment mechanism-based feasible strategies that simultaneously account for both adjustment magnitudes and conflict degrees, together with an algorithm for constructing such feasible strategies, and provide an illustrative example to demonstrate the validity and effectiveness of the proposed model.