標題: 分析層級程序法中屬性權重的統計估計式之探討
Statistical Estimators of Relative Weights for Uncertain Pairwise Comparison Data in the Analytic Hierarchy Process
作者: 鄭文英
Wen-Ying Cheng
張保隆
Pao-Long Chang
管理科學系所
關鍵字: 分析層級程序法;一致性指標;命題檢定;Analytic Hierarchy Process;Consistency Index;Hypotheses Test
公開日期: 1993
摘要:   在瞬息萬變的世界中,如何獲致有效的決策結果,是一刻不容緩的問 題。而分析層級程序法便是被廣泛應用的有效決策分析方法之一。分析層 級程序法透過下面四個步驟來處理決策問題:1.構建問題的決策層級;2. 收集各層級的成對比較矩陣;3.求算每一矩陣決策屬性元素的相對權重估 計值;4.結合各層級求算出的相對權重值,以求出各可選擇方案的綜合相 對權重,作為擇取最適方案的基準。但 Saaty 並對未針對不同的成對比 較資料特性,求估較適宜特定資料的決策屬性相對權重估計值,因此在本 文中將所收集得到的成對比較矩陣視為具隨機誤差值的輸入資料,在不同 的資料特性下,透過統計學中的推論方法,尋求更適切的屬性權重估計值 ,並進行資料偏好順序一致性的檢定,希望藉助統計方法與分析層級程序 法的結合,提供一更合理的決策規則。因此,在資料是決策者判斷依據前 提下,嘗試就不同的成對比較資料特性,以更合宜於由確定值形成成對比 較值資料特性的最小平方法和由區間值構成成對比較矩陣時以最佳線性不 偏估計法來求估屬性權重估計值,使估計值能更確切反應出未知的決策屬 性權重值。且以命題檢定來測試輸入矩陣中資料所呈現的權重順序一致性 程度,作為估計值使用與否的依據。最後,引入條件機率的概念來串聯層 級架構,求出各可選擇方案權重的估計值,以作為評選方案的參考。 The Analytic Hierarchy Process has found its way into various decision areas. To perform decision analysis using AHP includes four steps: setting up the decision hierarchy, collectin input data, using a estimation method to estimate the relative weights of decision elements, and arrive at a set of ratings for the decision alternatives. It provides a more systematic way to make a decision. In this paper, we intend to include the random errors of the judgements of pairwise comparison and the notion of randomness to strengthen AHP methodology. We focus on a least squares estimation and a best linear unbiased estimation of and compare statistical properties between Saaty's eigenvalue method vector of relative weights, and least squares method. We release the constraint that the input matrix must be a reciprocal one. And we take all the elements of input matrix to measure the consistency of input data. Furthermore, we construct the testing hypotheses for consistency index to analysis the reliability of the order of relative weights. Then, we apply these procedures in cases to illustrate how one can go through it.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT820457021
http://hdl.handle.net/11536/58214
Appears in Collections:Thesis