層級分析法的圖形一致性與目標規劃法

Graphical Consistency and Goal Programming Method for the Analytic Hierarchy Process

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。

In this study,we set out from the meaning of judgment matrix to point outthat its coefficients are perturbed measurement data of a preference structure, and then point out thatthe eigenvector methodfor judgment matrix analysis has sometheoretical weakness. In additions,theeigenvector 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 regressionnot only can take these ordering relations into consideration, also have nice properties in the decision theory. Therefore, analyzing the judgment matrix by using regressionis 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 thismethod with the most commonly used methods.