<p>The Decision-making trial and evaluation laboratory (DEMATEL) method and power average (PA) operator have been extensively applied to practical multi- attribute decision-making (MADM) problems. To extend the effective use of the traditional DEMATEL method and PA operator, we propose some improvements. First, instead of crisp numbers, the expert evaluates the level of the direct influence matrix for a DEMATEL problem using hesitant fuzzy linguistic term sets (HFLTSs). To derive the normalized direct influence matrix, we develop a data normalization method based on HFLTSs, which converts the HFLTSs into crisp numbers within [0,1] and the sum of them is equal to 1. On this basis, we design a weight determining method for attributes based on DEMATEL with HFLTSs. Second, given the limitations of existing HFLTSs in aggregating hesitant fuzzy linguistic information, we introduce an extended HFLTS and some relevant operator laws. We further define the hesitant fuzzy linguistic PA and hesitant fuzzy linguistic weighted PA (HFLWPA) operators, which reduce the adverse influence of abnormal hesitant fuzzy linguistic information. Subsequently, we integrate the DEMATEL with HFLTSs and the HFLWPA operator to propose a novel MADM&#xa0;approach based on DEMATEL and power aggregation operator under hesitant fuzzy linguistic contexts. Finally, the validity and rationality of the proposed approach are verified by a practical case of the selection of enterprise talents. The comparison and analysis shows the proposed model can obtain more valid and rational priority ranking of alternatives.</p>