Real options modeling, which extends the ability of option pricing models to evaluate real assets, can be used to evaluate risky projects because of its capacity to handle uncertainties. This research utilizes possibility theory to represent private risks of a project, which are not reflected in the market and hence are not fully evaluated by standard option pricing models. Using a transformation method, these private risks can be represented as fuzzy variables and then priced with a fuzzy real options model. This principle is demonstrated by valuing a brownfield redevelopment project using a prototype decision support system based on fuzzy real options. Because they generalize the original model and enable it to deal with additional uncertainties, fuzzy real options are entirely suitable for the evaluation of such projects.