With respect to multiple attribute decision making (MADM) problems in which the attribute weights take the form of real numbers, and the preference values take the form of uncertain linguistic variables, a new decision making analysis method is developed. By utilizing some operational laws of linguistic variables, we propose a new aggregation operators called ordered weighting C-LOWA (OWC-LOWA) operator based on the continuous LOWA operator(C-LOWA) and then develop an OWC-LOWA operator-based approach to MADM in uncertain linguistic setting. The approach is simple and don't need the comparison between two uncertain linguistic variables. Finally, an illustrative example about risk investment is given to verify the developed approach and to demonstrate its practicality and effectiveness.