Studied was multiple attribute decision making, in which the information about attribute weights is unknown completely and the attribute values and preference information on alternatives take the form of uncertain linguistic variables.  Operational laws of uncertain linguistic variables and a formula of possibility degree for the comparison between uncertain linguistic variables were introduced.  The concept of deviation degree between uncertain linguistic variables was defined.  A simple and exact formula based on the concept of combined method develop was developed, which can define be used to determine the attribute weights.  The uncertain linguistic weighting average (ULWA) operator was utilized to aggregate the uncertain linguistic variables corresponding to each alternative.  A possibility degree matrix (complementary judgement matrix) was constructed by the formula of possibility degree.  The alternatives were ranked by using the priority formula of complementary judgement matrixes and the most desirable one(s) was selected.  An illustrative example is given to highlight the procedure of the proposed algorithm.