Smart cities can be viewed as expansive systems that optimize operational quality and deliver a range of services, particularly in the realm of energy management. Identifying energy zones within smart cities marks an initial step towards ensuring equitable energy distribution driven by factors beyond energy considerations. This study introduces a socially oriented methodology for energy allocation during emergencies, implemented at the zone level to address justice concerns. The proposed method integrates a fuzzy leaky bucket model with an energy virtual buffer, leveraging extensive data from diverse city zones to allocate energy resources during emergent situations. By employing fuzzy sets and rules, the leaky bucket mechanism distributes buffered energy to zones, aiming to maximize energy utilization while promoting social justice principles. Evaluation of the approach utilizes consumption data from simulated smart city zones during energy-constrained emergencies, comparing it against a uniform allocation method. Results demonstrate the socially equitable allocation facilitated by the proposed methodology.