<p>Hesitancy degree plays a critical role in evaluating the indecisiveness of decision-makers (DMs). Many scholars have incorporated hesitancy degree into distance measures. Thus, selecting an appropriate hesitancy degree is particularly important. Compared with intuitionistic fuzzy sets and interval-valued fuzzy sets, hesitant fuzzy sets (HFSs) can more accurately capture the hesitation and varied preferences of DMs. However, existing definitions of hesitancy degree in HFSs still have certain limitations. To address this issue, this study proposes a novel dual-quantified hesitancy degree based on total deviation and range. Using the proposed measure, modified distance measures for HFSs are developed, and their theoretical properties are analyzed. Comparative experiments show that the proposed measures offer better performance than existing ones in terms of discrimination and expression accuracy. Furthermore, the novel distance measure is applied into the grey relational bidirectional projection (GRBP) method to improve its performance under a hesitant fuzzy environment. To illustrate the effectiveness of the proposed method, a numerical example is provided. The results of the comparative analysis show that the method distinguishes subtle differences between HFSs more effectively. Sensitivity analysis further confirms its stability. Overall, the proposed method significantly enhances the efficiency and accuracy of multi-attribute decision-making (MADM) in hesitant fuzzy environments, providing a more reliable tool for complex decision-making scenarios.</p>