In this paper, we study the multiple attribute decision making problems, in which the information about attribute weights is partly known and the attribute values take the form of linguistic variables or uncertain linguistic variables, and the decision maker has preferences on alternatives. We introduce the operation laws of linguistic variables and uncertain linguistic variables and a formula of possibility degree for the comparison between uncertain linguistic variables, and then define the concept of deviation degree between linguistic variables. We establish two goal programming models based on the concept of deviation degree under the situations where the attribute values are linguistic variables and uncertain linguistic variables respectively. By solving these two models, the attribute weights can be obtained. After that, when the attribute values are linguistic variables, we utilize the linguistic weighted averaging （LWA） operator to aggregate the given linguistic decision information, and then rank the ahematives and select the most desirable one（s）; when the attribute values are uncertain linguistic variables, we utilize the uncertain linguistic weighted averaging （ULWA） operator to aggregate the given uncertain linguistic decision information and utilize the formula of possibility degree to construct a possibility degree matrix （or called complementary judgement matrix）, and then utilize the priority formula of complementary judgement matrix to rank the alternatives and to select the most desirable one（s）. Finally, an illustrative example is also given