The increasing penetration of renewable energy and growing electricity demand in islanded microgrids have intensified the uncertainties on both the generation and load sides, posing severe challenges to their secure, stable, and economic operation. Traditional robust optimization methods, which over-emphasize extreme system conditions, often compromise operational economy. This paper employs fuzzy theory to generate stochastic optimization scenarios for the system. Based on the probability of scenario occurrence and the minimum hybrid energy storage system capacity required for each scenario, a scenario reduction process is conducted. A stochastic optimization-based dispatch method for islanded microgrids is proposed. The method involves establishing uncertainty models for renewable energy and load to generate stochastic scenarios, formulating a mathematical model, performing demand response dispatch under each scenario, and finally filtering out extreme scenarios. Based on the proposed method, experimental verification is carried out in an island microgrid case. The proposed method reduces the system operating cost by 20.17% compared to the traditional robust optimization approach. The results verify the effectiveness and superiority of the proposed method.