Abstract: A decision making method is proposed to deal with decision making problems with incomplete reciprocal judgment matrix which satisfies multiplicative consistency. Firstly, the definition of multiplicative consistent reciprocal judgment matrix is simplified and several other expressions of the definition are given. Furthermore, a method to compute missing elements of the incomplete judgment matrix from the special known n-1 elements is given. Then the acceptance conditions of incomplete reciprocal judgment matrix and the measurement and adjustment method of the matrix are presented. Then three decision making steps for incomplete reciprocal judgment matrix are given: the measurement and adjustment of the incomplete reciprocal judgment matrix consistency, the iterative process to calculate missing values of the incomplete reciprocal matrix and selection of the best alternative. Finally, a numerical example is given. Through the computation of this example and the comparison between the proposed method and the known method in other papers, it demonstrates that the solution process of the method proposed in this paper is simple and effective.

Key words: management science, decision making theory, iterative method, incomplete reciprocal judgment matrix, multiplicative consistency

摘要： 对于满足乘性一致性的残缺互补判断矩阵的决策问题,提出了一种决策方法。首先把互补判断矩阵的乘性一致性定义进行了简化,得到了互补判断矩阵乘性一致性的另外几种表达形式;进一步得到了在已知n-1个特殊元素的条件下,残缺互补判断矩阵中缺失元素的补全方法;然后给出了残缺互补判断矩阵可接受的条件,以及矩阵的一致性检验及调整方法;基于残缺互补判断矩阵,给出了以下决策步骤:残缺互补判断矩阵的一致性检验及调整过程,补全缺失元素的迭代过程和最优方案择优过程。最后给出了一个实例,通过该实例的计算以及本文方法与已有方法的比较,证明了本文方法是简便和有效的。

关键词: 管理科学, 决策理论, 迭代法, 残缺互补判断矩阵, 乘性一致性