As an extension of hesitant fuzzy linguistic and intuitionistic fuzzy linguistic, the hesitant-intuitionistic fuzzy linguistic set is proposed, and its score function, accuracy function and Hamming distance are also defined. In order to deal with uncertain multi-criteria decision-making problems under the hesitant-intuitionistic fuzzy linguistic environment, an extended VIKOR method based on the evidence theory and prospect theory is proposed. The evidence theory can well deal with the situation where the probability information is unknown. And the prospect theory takes bounded rationality into consideration, which can make the decision more realistic. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.