Scale-Extending Method for Constructing Judgment Matrix in the Analytic Hierarchy Process
Scale-Extending Method for Constructing Judgment Matrix in the Analytic Hierarchy Process
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作者：
Hu De-cai
层次分析法中的判断矩阵在实践中往往不能通过一致性检验，导致决策失败，而该问题至今仍未得到解决。本文实例说明，判断矩阵一致性检验误差的主要原因是传统的判断矩阵构造方法存在严重缺陷。使得判断尺度不变，使得在实践中存在差异的候选项目在构建判断矩阵的过程中变得没有差异。提出了一种构造判断矩阵的新方法——尺度扩展法。证明了无论何种判断尺度，新方法构造的判断矩阵始终是完全一致的。因此不需要一致性检验，并且可以很容易地得到重要性权重向量。新方法提高了层次分析法决策的可靠性，使层次分析法简单易用。
The judgment matrices in AHP often can not pass the consistency checking, which leads decision-making to failure in practice, and the problem has not been solved ultimately yet. The examples in this paper illustrate that the main factor of the consistency checking error of the judgment matrix is the serious fault existed in the traditional method for constructing judgment matrix. It makes the judgment scales unchangeable, results the candidate projects which are difference in practice become no difference in the process of constructing judgment matrix. A new method for constructing judgment matrix, called scale-extended method, is presented in this paper. It is proved that the judgment matrices are always full consistency constructed by the new method using whatever judgment scales. So it does not need consistency checking and the importance weight vector can be got easily. The new method enhances the reliability of decision-making of AHP, and makes the AHP simple and easy use.