以多層級神經網路改善完整成對比較矩陣之不可接受一致性

Multi-Layer Perception for Improving Unacceptable Consistency of Pairwise Comparison Matries

謝裕成(Yu-Cheng Hsieh)

指導教授 ： 胡宜中

中原大學/商學院/企業管理研究所/碩士(2010年)

https://doi.org/10.6840/cycu201000547

摘要

層級分析法以及網路程序分析法在操作上就一致性可接受的成對比較矩陣進行分析以獲取準則的相對權重，而一致性不可接受的成對比較矩陣則通常交由決策者再次進行修改以調整該矩陣之一致性比例至0.1以下，但此一做法在實務上，尤其是在發放網路問卷，不僅未必可行，也徒增決策者的困擾。在矩陣階數愈大的情況下，更是難以達成一致性可接受。因此，如何藉由適當的方法就一致性不可接受之成對比較矩陣，將其一致性比例調整至可接受，以避免重新發放問卷，便成為一個頗為值得探討的議題。
過去有一些學者就一致性不可接受成對比較矩陣提出改善一致性比例的方法，這些方法的發展雖然均有其理論基礎，但多以提出幾個簡例的方式說明，並無使用大量的實驗例來驗證，故無法得知一致性不可接受矩陣被調整後的平均一致性比例以及矩陣調整前後的平均差異，難以一窺其有效性。因此以大量的實驗例檢驗這些方法在各種不一致程度以及各種矩陣階數下的有效性是有其必要性的。一個理想的方法除了能達成一致性可接受外，也必須能使矩陣調整前後的差異愈小，這代表矩陣調整後漏失的資訊也相對愈少。就此，本研究採用以 Saaty尺度為基礎的差異衡量方式。
由於多層級神經網路在預測問題上一直扮演著重要的角色，而本研究之特色即在於以多層感知器為基礎發展一致性不可接受成對比較矩陣之改善模式，並使用一致性可接受之矩陣做為訓練集藉以調整多層感知器之連結權重。我們另提出矩陣元素調整規則，藉以局部調整而非完全調整矩陣元素。其目的在於與完全調整相較，檢驗各方法在局部調整下是否能夠有機會不但使平均一致性比例可被接受，而且也能找到更小的平均差異。
實驗結果顯示：(一) 多層感知器在高不一致性下不但平均一致性比例可被接受，而且與其他方法相較顯示可以有更小的平均差異；(二) 矩陣元素的調整個數和幅度是有可能影響各方法所產生平均一致性比例的大小，以及調整前後的平均差異，亦即在局部調整下是有可能會得到較佳的平均差異；(三) 在低不一致性下並未顯示有哪一種方法擁有特別突出的績效，但決策者或許可審慎採用 Harker 以及 Saaty 分別在 1987 與 2003年所提出之方法。整體而言，在一致性比例的改善上雖然並不存在最好的方法，但由實驗結果卻能建議決策者在成對比較矩陣處於高不一致性下，可考慮使用本研究所發展之多層感知器改善模式。

關鍵字

成對比較矩陣 ； 層級分析法 ； 多層級神經網路 ； Saaty 尺度 ； 一致性 ； 網路程序分析法

並列摘要

Analytic Hierarchy Process and the Analytic Network Process, in operation on
the acceptable consistency of pairwise comparison matrix analysis to obtain the relative weight of criteria, while the unacceptable consistency of pairwise comparison matrix is usually referred to the decision-makers to modify again to adjust the consistency ratio to be smaller than 0.1, but this approach in practice, especially in the network issued a questionnaire, not only may not be feasible, but also create more trouble for decision-makers. In the matrix the more the order of the case, is the more difficult to achieve acceptable consistency. Therefore, how to by means of appropriate method, with the unacceptable consistency of pairwise comparison matrix, adjust the ratio of consistency to be accept able and avoid re-issuing questionnaires, it is another issue worthy of research.
In the past, some scholars proposed methods to improve for the sake unacceptable consistency of pairwise comparison matrix method. While the development of these methods has its theoretical basis but more to make a few simple cases illustrate the means, do not use a lot of experiments cases to verify, so we cannot know the average consistency ratio and the average difference. It is difficult to understand the effectiveness of such methods when matrices with unacceptable consistency are improved. Therefore, a number of experiments to test their levels in a variety of inconsistent and under a variety of matrix order of effectiveness, are necessary. An ideal way to achieve consistency in addition to acceptable, but also to make the difference smaller before and after the adjustment of the matrix, which represents the matrix loses information after adjustment is relatively less. In this regard, this study applies Saaty scale-based differences in measurement.
As the Multi-Layer Perception (MLP) has been playing an important role in the prediction problems, the characteristics of this study lay in MLP-based development unacceptable consistency of pairwise comparison matrix and improvement process and use the acceptable consistency of pairwise comparison matrix as a training set to adjust the MLP connection weights. We also propose to partially adjust the rules of the matrix element, but not completely adjust. The purpose is compared with the complete adjustment and the methods whether to have the opportunity not only adjusted average consistency ratio can be accepted, but also find better small average difference in the partial adjustment of the matrix elements.
The results show that: (a) MLP in high inconsistency ratio, not only average consistency ratio can be accepted, but compared with other methods shown to have a smaller average difference; (b) the number matrix elements to be adjusted and the range for each method may affect the consistency ratio on average size, and the average difference before and after the adjustment. That is, the partial adjustment is likely to be better for the average difference ; (c) low inconsistency, there is no any ways to show a particularly remarkable performance, but decision-makers can carefully adopt Harker's method and Saaty's method propose in 1987 and 2003, respectively. Overall, there is no best way in improving matrix of ratio, but through the experiment result, we can suggest the decision-makers to use MLP improve the high inconsistency.

並列關鍵字

Analytic network process ； Analytic hierarchy process ； Consistency ； Multi-Layer perception ； Saaty scale ； Pairwise comparison matrix

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