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研究生:廖鴻儒
研究生(外文):Liao, Hung-Ru
論文名稱:AHP權重向量解法之理論性質與模擬實驗比較
論文名稱(外文):Theoretical and Experimental Comparisons on AHP Judgment Matrix Analysis Methods
指導教授:林高正林高正引用關係
學位類別:碩士
校院名稱:南台科技大學
系所名稱:科技管理研究所
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:中文
論文頁數:74
中文關鍵詞:層級分析法模糊關係圖形一致性限制穩健迴歸模擬實驗
外文關鍵詞:Analytic Hierarchy ProcessFuzzy relationsGraphical consistency constraintsRobust regressionSimulation experiment
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層級分析法,因其實施步驟與人們常用的分析步驟相近,目前已被廣泛地應用於工程與管理的各種不同領域,尤其是必需混合屬性與屬量分析的問題。林高正等人(2009a, b) 從判斷矩陣的意涵出發,指出它是一個偏好結構之受到擾動的量測資料,進而指出固有向量法EM 之理論漏洞與實務應用上的缺點。相對地,以迴歸分析為基礎的方法,除有不錯的理論性質外,還有許多實務應用上的優點。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。他們並定義了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,進而探討了加入圖形一致性限制之對數最小平方法LLSM-GC 與目標規劃法GPM-GC 的性質,以及它們與舊有權重向量解法之比較。然而,偏好量測是屬於心理量測,其量測誤差通常會有厚尾的現象。因此,採用穩健迴歸會比一般迴歸更為恰當。延續林高正等人(2009a, b) 的成果,本研究在探討以Huber 估計量求解權重向量,以及加入圖形一致性限制之Huber 權重向量的性質。考量到除Huber 估計量外,還有多種的M-估計量。因此,本研究採用基因演算法求解。本研究並透過模擬實驗分析相關權重向量解法之估計能力與估計行為。實驗結果顯示,在實驗誤差為對數常態分配與對數雙指數分配時,平均而言,LLSM-GC 與GPM-GC所得之因素排序顯著地比舊有的EM、LLSM 與GPM 更接近真正的因素排序。此外,本研究並以數值範例說明Saaty and Vargas 所指的保序性並非指保持真實權重的順序,以及CR 值檢定並不能充份偵測誤差的影響。
The analytic hierarchy process (AHP) is one of the most commonly applied multi-attributes decision analysis techniques, for the reason that its implementation steps are similar to commonly used analysis steps of people. It is even more popular in cases that quantitative and qualitative attributes combine. Lin et al. (2009a, b) set out from the meaning of a judgment matrix, pointed out that its coefficients are perturbed measurement data of a preference structure, and then showed that Saaty’s eigenvector method has some theoretical weakness and practical disadvantages. On contrast, the methods based on statistical regression not only have nice properties in the decision theory, but also have several practical advantages. Therefore, analyzing the judgment matrix by regression is more proper. In additions, they defined the graphical consistency and the graphical consistency constraints of a judgment matrix,
then considered the theoretical properties of the logarithm least squares method and the goal programming method with the graphical consistency constraints, and compare theses two methods with the most commonly used methods. It is found that these two methods have nice properties and several practical advantages. However,
measuring a preference structure is a psychological measurement, its error term usually has a heavy tail. Therefore, it is more proper to use robust regression than ordinal regression. Based on the results of Lin et al (2009a, b), in this study, we consider the Huber estimator of the priority vector and the case with graphical
consistency constraints. We solve the related optimization problem by using genetic algorithms. These algorithms can be easily modified for solving another M-estimator. In additions, since finding the priority vector is a problem of statistical estimation, the
behavior and the ability of the estimators are as important as their theoretical properties. In this study, we perform a factorial experiment to test the related methods, for the cases that the logarithms of error terms are normally distributed or
double-exponentially distributed. From the experimental results, it is found that LLSM-GC and GPM-GC perform better in finding the priority order than the traditional methods. In additions, in this experiment we have also found examples for demonstrating that the priority order found by EM is not the true order, and testing the
consistency of a judgment matrix by using CR-value is not a serious method.
摘要............................................................................................................................ iv
ABSTRACT.................................................................................................................v
誌謝............................................................................................................................ vi
目錄........................................................................................................................... vii
表目錄...................................................................................................................... viii
圖目錄........................................................................................................................ ix
第一章 緒論
1.1 研究背景與動機...............................................................................1
1.2 研究目的...........................................................................................2
1.3 研究流程...........................................................................................3
1.4 章節簡介...........................................................................................4
第二章 文獻探討
2.1 層級分析法.......................................................................................6
2.2 AHP 權重向量解法..........................................................................9
2.2.1 固有向量法............................................................................9
2.2.2 對數最小平方法與目標規劃法..........................................10
2.2.3 加入圖形一致性之對數最小平方法與目標規劃法..........12
2.3 權重向量解法之理論性質比較.....................................................15
第三章 結合穩健迴歸與模糊關係的權重向量解法
3.1 穩健迴歸.........................................................................................20
3.2 基因演算法.....................................................................................24
3.3 數值範例.........................................................................................27
3.4 本章結論.........................................................................................32
第四章 數值模擬實驗
4.1 實驗設計.........................................................................................33
4.2 實驗結果-對數常態誤差...............................................................36
4.3 實驗結果-對數雙指數誤差...........................................................41
4.4 本章結論.........................................................................................46
第五章 結論與後續研究方向
5.1 結論.................................................................................................48
5.2 後續研究方向.................................................................................49
參考文獻....................................................................................................................51
附錄A 以基因演算法求解Huber 權重向量之MATLAB 程式碼.................55
附錄B 以基因演算法求解Huber-GC 權重向量之MATLAB 程式碼..........65
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