This paper applies double-uncertainty optimization theory to the operation of AC/DC hybrid microgrids to deal with uncertainties caused by a high proportion of intermittent energy sources. A fuzzy stochastic expectation economic model for day-ahead scheduling based on uncertain optimization theory is proposed to minimize the operational costs of hybrid AC/DC microgrids. The fuzzy stochastic alternating direction multiplier method is proposed to solve the double-uncertainty optimization problem. A real-time intra-day unbalanced power adjustment model is established to minimize real-time adjustment costs. Through comparative analysis of deterministic optimization, stochastic optimization and fuzzy stochastic optimization of day-ahead scheduling and real-time adjustment, the validity of fuzzy stochastic optimization based on a fuzzy stochastic expectation model is proved.