Most of the existing studies on multi-attribute decision making problems of evaluation index prioritiza- tion have not taken the prioritized degrees (the importance degree) into account, which usually plays a construc- tive role in the comprehensive evaluation results. This paper tries to develop an effective method for solving mul- ti-attribute decision making problems, considering not only the prioritization relationship but also the prioritized degrees. Firstly, the prioritized averaging operator was improved. Moreover, the membership degree functions were constructed and the prioritized averaging operator considering the prioritization and prioritized degree of in- dicators simultaneously was proposed. Finally, an example of the comprehensive evaluation of integrated logistics enterprise level was given to prove the validity and superiority of the proposed models and method.