使用灰關聯分析改善模糊成對比較矩陣不可接受之一致性

Grey Relational Analysis for Improving Unacceptable Consistency of Fuzzy Pairwise Comparison Matrices

徐銘澤(Ming-Tse Hsu)

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/cycu201000546

摘要

層級分析法，是一個廣為應用在不確定及多屬性的情況下的決策工具。其方式是利用成對比較進行構面間、準則間以及方案間的成對比較，以求出準則與方案的相對權重，從而找出適當的計畫。為確保受訪者所做判斷具有前後一致性，避免不一致決策的產生，所有的成對比較矩陣均須進行一致性檢定。然而，一致性在實務上不易達成，當成對比較矩陣階數越大時，不一致的情形愈容易發生；要求受訪者重新填寫不但增加受訪者困擾也未必可行，為使回收之問卷被充分利用，適當地改善成對比較矩陣的品質，將矩陣轉變為一致性小於0.1、成為可接受的問卷，是一個值得探討的議題。
由於模糊集合能處理主觀認知上的不確定性，可融入受訪者的感認，較傳統Saaty尺度在語意的處理上更有彈性，因此模糊成對比較矩陣的使用及其不一致性之改善在層級分析法以及網路程序分析法上便成為重要的研究議題。本研究之特色及在於灰關聯分析為基礎發展一致性不可接受之模糊矩陣的改善模式。過去在改善一致性也有一些學者提出其他方法，但多以簡例說明，並未以大量實驗例佐證，難以一窺其有效性；並且多未能提出改善前後資訊保留的多寡，本研究以其它七種改善一致性的方法和灰關聯分析的效果做比較，觀察保留原矩陣的資訊何者方法較佳，並做為方法之間績效評估的標準。
研究結果發現 (一) 相似度最大的比較數列之灰關聯度未必相對最大，因此我們找出最佳方案與灰關聯方析偏好的平均名次 (二) 越到高階時，在各個不一致性區間其平均名次越相近，且灰關聯分析在低度不一致性對最佳方案的篩選有最大的正相關性，不一致性越高則越低。(三) 相較於其他方法，三、四階時能找出最好的最佳方案，並和灰關聯分析排序高低有最多的相關性。藉由以上實驗觀察結果，找出最佳比較數列和灰關聯分析方案評選之間的關係。

關鍵字

網路程序分析法 ； 灰關聯分析 ； 層級分析法 ； 模糊集合 ； 成對比較矩陣 ； 一致性比例

並列摘要

Under uncertainty and multi-attribute, Analytic Hierarchy Process (AHP) is the applied decision-making tool. AHP uses the pairwise comparison among widely aspects, criteria, and alternatives to get the relative weight, and finds the best aspect, criterion, or alternative. In the cause of avoiding resulting inconsistency, all of the pairwise comparison matrixes have to test their consistency. However, in the practices, the consistency is hard to achieve. Because when the orders of pairwise comparison matrixes is larger and larger, the inconsistency is easier to occur. So, not only how to let the all questionnaires can be utilized adequately, but how to appropriately improve the quality of pairwise comparison matrix to let its consistency can be less than 0.1 is worth discussing issue.
Due to fuzzy sets can deal with the uncertainty of subjective cognition and respondents’ perception, in addition, it has more flexibility on linguistic than the Saaty scale, so, for the AHP and ANP (Analytic Network Process), the fuzzy pairwise comparison matrix that improves the inconsistency is the important research issue. The main purpose of our study is to take the Grey Relational Analysis (GRA) as the base to built improvement model of fuzzy matrix of unacceptable consistency. In the past, some scholars also bring up other methods to improve the consistency, but they just take some simple examples to explain, not a large number of experiment examples to evidence, so, it’s difficult to know the effectiveness. We take seven methods which can improve consistency to compare with the result of GRA to observe that which method is the best for keeping the information of original matrix, and as the standard of performance evaluation among methods.
Our results are: (1) The comparative sequences are the most similar, but their Grey Relational Grades (GRG) are not necessarily relatively the most. So, we find the best alternative and the ranking GRA preferred; (2) When the orders is more, the ranking is closer for every inconsistency interval. On the other hand, when GRA is the low inconsistency, it has the most positive correlation for selecting the best alternative, and vice versa; (3) Compared to other methods, when orders is three or four, it can find the best alternative, and has the most correlation for the ranking of GRA. By the results, our study finds the relationship between the best comparative sequences and the alternative evaluation of GRA.

並列關鍵字

Analytic Network Process ； Fuzzy Sets ； Pairewise Comparison Matrix ； Consistency Ratio ； Analytic Hierarchy Process ； Grey Relational Analysis

參考文獻

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