Abstract Motivated by a real-world case, this paper deals with uncertainty issues in the resilient and sustainable electricity supply chain network design. Uncertainty is always found in electricity demand prediction and perfect foresight is not possible. The resilience of electricity networks in face of uncertainty can prevent catastrophic impacts. Besides, due to the growing concerns about social impacts, considering social measures along with the other measures is becoming critical when analyzing the network costs. In this paper, a multi-objective optimization model is developed, which consists of the total cost in the first objective, resiliency measures in the second objective, and some aspects of corporate social responsibility in the third objective. The resiliency measures minimize de-resiliency, including successive establishment, distributed generators inadequacy, congestion through electrical lines, and energy dissatisfaction level. A novel robust approach is also proposed to deal with the uncertainty of electricity demand based on the light robust programming and possibilistic theory in the fuzzy logic. By investigating a real case in Iran, the contributions of the considered measures, and the effects of uncertainty are analyzed. The analyses reveal that by applying the proposed model the decision-makers can enhance corporate social responsibility and resiliency by 50% and 20%, respectively, although it increases the total cost by 50%. Moreover, the results of applying the proposed fuzzy-robust approach show that how the decision-makers can effectively allocate the uncertainty budget and protection level to attain more robust solutions in terms of standard deviation and mean value of the total cost.