The differential evolution (DE) algorithm is a powerful search technique for solving global optimization problems over continuous space. The search initialization for this algorithm is handled stochastically and therefore does not adequately capture vague preliminary knowledge. This paper proposes a novel Fuzzy Differential Evolution (FDE) algorithm, as an alternative approach, where the vague information on the search space can be represented and used to deliver a more focused search. The proposed FDE algorithm utilizes (a) fuzzy numbers to represent vague knowledge and (b) random alpha-cut levels for the search initialization. The alpha-cut intervals created during the initialization are used for fuzzy interval based mutation in successive search iterations. Four benchmark functions are used to demonstrate performance of the new FDE and its practical value. Additionally, the application of the FDE algorithm is illustrated through a reservoir operation case study problem. The new algorithm shows faster convergence in most of these functions.