Voltage sag and voltage unbalance can be considered as the major power quality concerns in low voltage distribution networks. A dynamic voltage restorer (DVR) is commonly used to provide voltage support for load buses containing critical loads. In practice, however, the limited power capacity of these devices can highly deteriorate the desirable regulation expected from them, especially under severe disturbances. This paper proposes an efficient fuzzy logic based capacity management scheme for DVRs in mitigating voltage disturbances. The strategy can appropriately organize the DVR operation complying with the features and priorities given by the designer. A novel approach to derive the compensation reference signals is presented in which the mitigation factors associated with the disturbances are adjusted by the fuzzy scheme. Further, a single-step prediction horizon technique is implemented to regulate the switching commands of the DVR. Various simulation cases are studied in MATLAB to demonstrate efficacy of the proposal.