<p>Dual hesitant fuzzy elements can simultaneously capture the hesitancy and uncertainty of information. Although significant progress has been made in dual hesitant fuzzy elements aggregation for multi-attribute decision-making, existing aggregation operators still lack idempotency, potentially leading to biased decision outcomes. To address this issue, this study proposes a series of novel dual hesitant fuzzy elements aggregation operators, and further establishes a corresponding decision-making method. Specifically, we firstly propose two normalized Einstein operations for dual hesitant fuzzy elements and define a novel comparison rule. Furthermore, several normalized Einstein aggregation operators are developed based on the provided normalized Einstein operations. What’s more, we establish a decision-making method for solving practical multi-attribute decision-making problems. In addition, two practical cases are conducted to demonstrate the feasibility and practicality of our method.</p>