層級分析法的圖形一致性與目標規劃法

本研究從層級分析法判斷矩陣之意涵出發，指出判斷矩陣是一個偏好結構之受到擾動的量測資料，進而指出以固有向量法為基礎進行判斷矩陣分析的理論漏洞。另外，對於從實務上或判斷矩陣中所找出的權重大小順序，固有向量法也無法充分予以考慮。相對地，以統計迴歸分析為基礎的方法，除較容易整合額外的權重大小順序限制外，也有不錯的決策理論性質。因此，以迴歸分析為基礎應是進行判斷矩陣分析較佳的方向。此外，由於判斷矩陣是用以表示偏好結構，它可以改用模糊關係表示。而利用所對應之模糊關係的截集，可定義判斷矩陣的圖形一致性與求解權重向量時的圖形一致性限制。本研究並探討了加入圖形一致性限制之目標規劃法的求解與理論性質，以及它與現有權重向量主要解法之比較。

關鍵字

層級分析法；對數最小平方法；目標規劃法；模糊排序關係；圖形一致性

並列摘要

In this study, we set out from the meaning of judgment matrix to point out that its coefficients are perturbed measurement data of a preference structure, and then point out that the eigenvector method for judgment matrix analysis has some theoretical weakness. In additions, the eigenvector method cannot take the ordering relations of priority weights, found in the practice or from the matrix, into consideration. On contrast, the methods based on statistical regression not only can take these ordering relations into consideration, also have nice properties in the decision theory. Therefore, analyzing the judgment matrix by using regression is more proper. Moreover, since the judgment matrix is used to represent a preference structure, it can be replaced by a fuzzy relation. Using the cut sets of the associated fuzzy relation, we define the graphical consistency and the graphical consistency constraints of a judgment matrix, then we consider the solution method and theoretical properties of the goal programming method with the graphical consistency constraints, and compare this method with the most commonly used methods.

並列關鍵字

Analytic Hierarchy Process (AHP) ； Logarithm least square method ； Goal programming method ； Fuzzy ordering relation ； Graphical consistency

參考文獻

Bryson, N. (1995), A goal programming method for generating priority vectors, Journal of Operational Research Society 46 (5), 641-648. doi: 10.2307/2584536

Chandran, B., Golden, B., and Wasil, E. (2005), Linear programming models for estimating weights in the analytic hierarchy process, Computers and Operations Research 32 (9), 2235-2254. doi: 10.1016/j.cor.2004.02.010

De Jong, P. (1984), A statistical approach to Saaty’s scaling method for priorities, Journal of Mathematical Psychology 28, 467-478. doi: 10.1016/0022-2496(84)90013-0

Dyer, J.S. (1990), Remarks on the analytic hierarchy process, Management Science 36 (3), 249-258. (Responses appear in 36 (3), 259-273.) doi: 10.1287/mnsc.36.3.249

Fichtner, J. (1986), On deriving priority vectors from matrices of pairwise comparisons, Socio-Economic Planning Sciences 20 (6), 341-345. doi: 10.1016/0038-0121(86)90045-5

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層級分析法的圖形一致性與目標規劃法

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