互补判断矩阵一致性改进方法

Improving Method for the Consistency of Reciprocal Judgement Matrix

关于两两方案比较的偏好信息形式的决策问题是决策分析中的一个重要课题·其中决策者给出的判断矩阵是否具有一致性是一个很重要的问题,它直接影响到由判断矩阵得到的排序向量是否能真实地反映各比较方案之间的客观排序·针对决策者给出的关于决策方案的一类互补判断矩阵,提出了一种新的改进判断矩阵一致性的方法·首先,给出了关于互补判断矩阵及其满意一致性的定义,同时还通过建立可达矩阵给出了互补判断矩阵满意一致性的判定方法;然后通过构造和分析一种偏差矩阵,给出了将互补判断矩阵改进为满意一致性矩阵的计算步骤·最后给出了一个算例·

An important process in decision analysis is to study the decision making problem with pairwise comparison information on alternatives. Whether the judgement matrix given by DM has satisfying consistency is an important thing, because it directly influent if the ranking result can reflect the truth ranking about alternatives. A new method was presented to improve the consistency of the reciprocal judgement matrix about the alternatives provided by the decision maker. Firstly, the definitions about the reciprocal judgement matrix and its satisfying consistency were given. At same time, a judgement approach to the reciprocal judgement matrix was also given by establishing the reachable matrix. Then, by constructing and analyzing the deviation matrix, computational way of adjusting the reciprocal judgement matrix into the satisfying consistency was proposed. Finally, a numerical example was given to illustrate the effectiveness of the proposed method.