Abstract: To solve the group decision making problems with uncertain linguistic multiple attributes and incomplete information on attribute weights, a decision analysis method was proposed. Describing the uncertain linguistic variables, the calculating steps were given to solve the group decision making problems, among which the core was to aggregate the uncertain linguistic decision matrices provided by experts to a group decision matrix with informative possibility. Then, a quadratic programming model was developed through calculating the deviation values between every alternative and positive/negative ideal point to determine attribute weights, thus giving the relative proximity of each alternative so as to rank all alternatives. A numerical example was given to illustrate how to use the proposed method and the analysis result showed that the method is simple, feasible and easy to perform.