Cournot duopoly with yield uncertainty is of interest both from a theoretical standpoint and a practical standpoint. In many sectors of economy, the actual products produced and the targeted quantities do not coincide. Commonly, random variables are used to model yield uncertainty. However, the models with random yields have a known drawback. When the number of firms greater than three, the expected firm’s profit first increases when level of uncertainty (i.e.,variance of a random variable) increases and then decreases. When the number of firms no greater than three, there is no that drawback, the expected firm’s profit always decreases when level of uncertainty increases. In this paper, fuzzy sets are used for the first time to model Cournot competition in the presence of yield uncertainty. This article deals both with Cournot oligo­poly with fuzzy yields and Cournot oligopoly with fuzzy random yields. In the fuzzy random approach, probabilistic methods and fuzzy methods are combined. In this paper, equilibrium quantities and expected firms’ profits are found. For models with fuzzy yield, the drawback mentioned above is absent. For any number of firms, expected profit of a firm decreases when level of uncertainty increases. Also, in the fuzzy random approach, Cournot duopoly in which one firm is overconfident is studied. That firm forecasts the quantity produced unreasonably accurately. For this case, equilibrium quantities and expected firms’ profits are also presented in the paper.