Abstract: In order to overcome the drawbacks that inference information accuracy is poor and integration outcome validity remains to be discussed resulting from measurement scale selection and knowledge matrix solution in traditional DS/AHP method, the existing problems are presented by analyzing the traditional modeling approach. The complementary judgment matrix is introduced to extract decision maker’s relative preference inferences between alternative teams and frame of discernment. After that, a transformation theorem from knowledge matrix with incomplete and complementary information to BPA function is proposed, as well as an improved method is established to perform inference and judgment in terms of evidence discounting idea and evidence combination rule. A numerical example is applied to illustrate the operational process of the presented method.

Key words: Dempster-Shafer/Analytic Hierarchy Process（DS/AHP）, complementary judgment matrix, evidence theory, analytic hierarchy process, basic probability assignments

摘要： 为克服传统DS/AHP方法中因度量标度选择问题和知识矩阵求解问题而带来的推断信息精确性差和集成结果有效性有待商榷的缺陷，结合传统方法的建模思路分析指出其中存在的问题，通过引入互补判断矩阵提取决策者对方案组与识别框架之间的相对偏好推断，在此基础上提出由残缺互补知识矩阵向BPA函数转换的定理，并结合证据折扣思想和证据组合规则构建了开展推理判断的改进方法步骤，应用一个算例说明了提出方法的具体操作过程。

关键词: 登普斯特谢菲尔/层次分析方法（DS/AHP）, 互补判断矩阵, 证据理论, 层次分析法, 基本概率分配