Decision-making in strategic conflicts often involves uncertain preferences. Triangular fuzzy preferences offer an intuitive and flexible representation of uncertainty. Therefore, this study aims to incorporate triangular fuzzy preferences into the graph model for conflict resolution (GMCR). A new framework for GMCR with two decision-makers (DMs) is developed, integrating triangular fuzzy preference relations to represent and analyze conflicts under uncertainty. Within the framework, four basic stability definitions are extended for two DMs to model with triangular fuzzy preferences. More specifically, triangular fuzzy Nash stability, triangular fuzzy general metarationality, triangular fuzzy symmetric metarationality and triangular fuzzy sequential stability provide a comprehensive description of human behavior patterns. A state is triangular fuzzy stable for a DM if there is no reward to leave the state, where reward is assessed according to triangular fuzzy relative strength of preference (TFRSP) and triangular fuzzy satisficing threshold (TFST). Furthermore, a triangular fuzzy equilibrium, which is triangular fuzzy stable for all DMs, represents a possible solution to the strategic conflict. Finally, an illustrative example is applied to demonstrate the applicability of the proposed framework in practice.