一种提高判断矩阵一致性程度的方法

 层次分析法是一种实用的多维决策方法。在运用层次分析法的过程中，需要对判断矩阵进行一致性检验。若检验不能通过，则应尽可能小幅度地调整部分元素后再检验，从而达到既能最大程度地保留原有信息又能提高矩阵的一致性程度的目的。目前，许多学者提出了提高判断矩阵一致性程度的多种方法，但这些方法的局限性是有时某些元素调整前后的变化太大，且需调整的元素较多，这显然违背了决策者的最初意愿。本文提出由判断矩阵中行列对应元素乘积的算术平均值与相应元素偏差的最大值来判别与调整不合理元素，进而提高判断矩阵一致性程度的方法。该方法可预先设定调整幅度，最大程度地保留原有信息。不合理元素的判别方法具有简洁、有效、快速的特点。整个调整过程计算简单，既可人工也可利用计算机进行。

A Method in Regulating the Consistency of the Judgment Matrix

While making decision by Analytic Hierarchy Process (AHP), the consistency of judgement matrix must be checked. If it can not pass the test, some entries of the judgement matrix should be adjusted, and the consistency should be tested again. Accordingly, it is important to find methods regulating the consistency of the judgment matrix. However, with many such methods, the variations of many entries are too great, and the number of adjusted entries are too large, as is not very convenient for decision-makers. This paper proposes a method for regulating the consistency of the judgment matrix, where the revision and the identification of error-elements are based on the maximum deviation of the related element to the arithmetic mean obtained from multiplying a row vector by a column vector. This method can better describe the information of the original judgment matrix, and the threshold of the regulation can also be pre-established. The unreasonable elements can be identified easily, efficiently and quickly. The computation is simple, and the regulation can be done manually or by computer.