Preference relations (PRs) are an effective tool to express people's opinions over alternatives. But it is usually difficult to give accurate information using crisp numbers. The main purpose of this paper is to propose the complementary triangular hesitant fuzzy preference relations (CTHFPRs) to solve the above correlative problem. Two aggregation operators are defined and some of their properties are discussed. In addition, we give the definition of consistency and propose two methods to measure consistency for the presented preference relations. Next, a decision-making approach under triangular hesitant fuzzy environment is constructed and a numerical examples is provided to illustrate the availability of the proposed PRs and consistency measure methods.