Abstract: This paper first proposes the distance definition between a reciprocal judgement matrix and the set of consistent reciprocal judgement matrices, based on which a new consistency index of reciprocal judgement matrix and the measure method of it are proposed, which is the similarity degree between the goal matrix and the consistent matrix constructed based on the goal matrix. For those judgement matrix that don't meet this consistency index, an iterative algorithm is introduced to enhance its consistent degree. One theorem gives the conclusion that the revised judgement matrix which is built after some times of iterations must meet the consistent degree required. In the group decision making section, a theorem gives the conclusion that if several individual judgement matrix all meet the consistent degree demand, then the consistency index of the group judgement matrix constructed based on the individual judgement matrix has a deterministic low limit. Another theorem also proves that if the similarity degree between each individual judgement matrix and the given judgement has one common low limit, then the similarity degree between the group judgement matrix which is constructed based on all the individual judgement matrix and the given judgement matrix has one deterministic low limit. All the conclusions are the basis for the application of the consistency index to group decision making problems. Finally, some examples are given to show the feasibility and efficiency of the algorithm and relevant conclusions in group decision making.

Key words: reciprocal judgement matrix, shortest distance, consistency index, iterative algorithm

摘要： 首先给出了互反判断矩阵与一致性互反判断矩阵集之间距离的定义,基于此定义,提出了一个新的互反判断矩阵一致性指标,并给出了此一致性指标的度量方法。对于不满足此一致性指标的互反判断矩阵,提出了一个迭代算法来提高其一致性程度。得出了群体互反判断矩阵一致性指标的下界,为提出的一致性指标应用于群决策问题提供了理论基础。最后用数值例子说明了该迭代算法的可行性和有效性以及群决策中的相关结论。

关键词: 互反判断矩阵, 最短距离, 一致性指标, 迭代算法