This paper proposes a new cross-efficiency model called Regret Cross-Efficiency Model using Attitudinal Entropy Approach (RACE) to address limitations of existing Data Envelopment Analysis (DEA) methods. RACE incorporates regret theory and attitudinal entropy to synthesize cross-efficiencies under incomplete rationality, providing a more comprehensive and robust ranking of Decision Making Units (DMUs). Empirical examples demonstrate the validity and robustness of the RACE method.