The main idea of this paper is to present a method for offering a power generation rate of wind power plants in the electricity market in the conditions, in which there is a lack or extreme shortage of information. In such a state, methods conventionally used in normal conditions are no more applicable. The methods that have been formerly presented for the conditions with severe uncertainty are mostly applied in local decision making, but in the method proposed in this paper, global decision making is considered. The proposed method is based on Liu's uncertainty theory, and the information related to uncertain variables is provided by experts. After developing a cumulative distribution function for expert data, Liu's distribution is calculated. Then, the values of uncertain variables are determined based on various belief degrees. After converting the uncertain model of the objective function into a certain equivalent model in the Liu space, the profit function should be maximized via the two-stage stochastic programming method. The data used are real and relevant to the Nord Pool market. Investigation of the simulation results for two different and specific days indicates the efficiency of the proposed strategy.