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The multi-attribute decision making problems are studied, in which the information about the attribute values takes the form of uncertain linguistic variables, and the information about attribute weights is incompletely known. The concept of deviation degree between uncertain linguistic variables is defined, and ideal point of uncertain linguistic decision making matrix is also defined. A formula of possibility degree for the comparison among uncertain linguistic variables is introduced. Based on the deviation degree and ideal point of uncertain linguistic variables, an optimization model is established to determine the weights, and then to aggregate the given uncertain linguistic decision information. A method based on possibility degree is given to rank the alternatives. Finally, an illustrative example is also given.