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In the problem of group decision-making, the information about the decision makers' preferences is not complete due to factors of the quality of human resource and the influence of environment. The information gained by decision making can be loss or hazy. When it is hazy the values of the objects to be appraised are interval grey numbers. The group decision making problems including the grey number are called the grey group decision-making problems. Combining the thoughts and methods of the grey system with the classic group decision-making theory, the grey group decision making problems are discussed. In this paper, we develop a GREY DEMATEL method for group decision-making to gather group ideas and analyze the cause-effect relationship of complex problems in grey environments. Procedures of the GREY DEMATEL method are then proposed. Using the GREY DEMATEL procedures, the involved criteria of a system (or subsystem) are separated into the cause and effect groups for helping decision-makers focus on those criteria that provide great influence. Finally, a practical example is used to show feasibility and effectiveness of the proposed approach.