Data Envelopment Analysis (DEA) is a well-established nonparametric method for evaluating the relative efficiency of Decision-Making Units (DMUs). Conventional DEA models assume deterministic input and output data, which is rarely the case in real-world applications characterized by uncertainty and ambiguity. To overcome this limitation, this paper proposes a new fuzzy DEA framework by developing a modified efficiency function that is able to explicitly incorporate data uncertainty through fuzzy numbers. A new weighted cut-based efficiency measure is introduced, which transforms the fuzzy DEA model into an equivalent deterministic linear programming formulation. The theoretical properties of the proposed model, including feasibility, uniformity, and boundedness, are investigated. Numerical experiments based on simulated data demonstrate the effectiveness and robustness of the proposed approach compared with classical DEA and existing fuzzy DEA models. The proposed framework provides a flexible and reliable tool for evaluating efficiency in uncertain environments.