A crucial challenge for global query optimization in a multidatabase system (MDBS) is that some local optimization information, such as local cost parameters, may not be accurately known at the global level because of local autonomy. Traditional query optimization techniques using a crisp cost model may not be suitable for an MDBS because precise information is required. In this paper we present a new approach that performs global query optimization using a fuzzy cost model that allows fuzzy information. We suggest methods for establishing a fuzzy cost model and introduce a fuzzy optimization criterion that can be used with a fuzzy cost model. We discuss the relationship between the fuzzy optimization approach and the traditional (crisp) optimization approach and show that the former has a better chance to find a good execution strategy for a query in an MDBS environment, but its complexity may grow exponentially compared with the complexity of the later. To reduce the complexity, we suggest to use so-called k-approximate fuzzy values to approximate all fuzzy values during fuzzy query optimization. It is proven that the improved fuzzy approach has the same order of complexity as the crisp approach.