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研究生:梁德昭
研究生(外文):LIANG, DE-ZHAO
論文名稱:『層級分析程序』之缺點及改良
論文名稱(外文):SOME WEAKNESSES OF ANALYTIC HIERARCHY PROCESS AND A PROPOSED MODIFICATION
指導教授:葉若春葉若春引用關係
指導教授(外文):YE, RUO-CHUN
學位類別:博士
校院名稱:淡江大學
系所名稱:管理科學研究所
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
論文出版年:1990
畢業學年度:79
語文別:中文
論文頁數:134
中文關鍵詞:層級分析程序評分問題倒序現象一致性比值成對比較矩陣權重向量
外文關鍵詞:ANALYTIC HIERARCHY PROCESSGRADING PROBLEMRANK REVERSALCONSISTENCY RATIOPAIRWISE COMPARISON MATRIXTHE RELATIVE WEIGHTS OF THE CR
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A complex decision problem is usually characterized by a large number of
interacting factors,the major concerns being (1) how to properly assess
the importance of these factors to make trade-offs among them;and (2) how
to derive a systematic approach,by which the scores or the weights of the
alternatives can be obtained under the circumstances of a multiple
criteria decision.
In this dessertation,a Modified Analytic Process(MAHP) is proposed,which
is a decision analysis process consisting of value judgments of
alternatives,pairwise comparisons among criteria,and a hierarchic
comprsition for synthesizing results. Compared with the Analytic Hierarchy
Process(AHP),which is proposed by Saaty,not only the distributing
problem,but also the grading problem can be dealt with using
MAHP.However,in AHP only the distributing problem can be dealt with.About
the controversies of rank reversal in AHP,a reasonable inerpretation is
also given.From the interpretion,the effect of compensation among criteria
can be seen. Consequently ,there is no rank reversal in MAHP.
In addition,for the inconsistency of a pairwise comparison matrix,instead
of Saaty''s consistency ratio measure,a detection proceduremwhich is
proposed in this dessertation,is employed to detect the inconsistency.To
elicit the relative weights of the criteria from a pairwise comparison
matrix,an alternative method when the judgment values are limited by the
bounds of the scale,and/or when two coles objects are compared using a
integer scale.Lasttly,a demonstrated example(a solid waste study )will be
given to show how to employ MAHP in multiple criteria decision analysis.
一個複雜的決策問題,往往必須考量到許多互動的影響因素。是以,本文之主旨即著
重於探討:一、如何適切地衡量各因素之於決策目標的相對重要程度,以協調在各因
素上所作的考量與分析;二、尋求一套能在多評選標準的情境中,整合出各替選方案
之分數或權重的糸統化方法。
作者在這篇論文中,提出了一套改良的層級分析程序(Modifide Analytic Hierarchy
Process,MAHP)
,此程序為一決策分析程序,包含了對各替選方案的價值評判、評選標準間的相互比較
、以及分析結果的層級合併。相較於Saaty教授所發展的層級分析程序(Analytic
Hierarchy Process,AHP),AHP 僅能處理分配問題(Distributing
Problem),而MAHP則除了分配問題外,尚能處理評分問題(Grading
Problem)。再者,就AHP在倒序現象(Rank
Reversal)上所引起的爭議,亦嘗試於文中提出一合理的解釋;透過此一解釋,吾人
可觀察到在評選準間,就其對決策目標的重要性,彼此相互補償替代的現象與效果。
基於此一認識,謹慎而正確地運用MAHP,將不會遭致倒序現象的困擾。
此外,為了保證一成對比較矩陣(Pairwise Comparison
Matrix)能具有可接受的一致受程度,作者文中提出了一套偵測不一致性的偵測不一
致性的偵測程序,以取代Saaty 教授於AHP中所採用的一致性比值(Consistency
Ratio) 又當顧及在作成對比較時,其比值的裁定,常囿於整數尺度及其範圍的限制
,本文亦提出一套從成對比較矩陣中求取權重向量的演算法,該演算法能在上述的限
制下,較諸已往的特徵向量法(Eigenvector
Method),對權重向量有更為精確的估計。最後,為了說明如何把MAHP
運用在一個多評選標準決策問題的決策分析上,在第五章中採用一個假想的廢棄物處
理方式之規劃問題,以作為一簡單的操作範例。
TABL OF CONTENTS
ABSTRACT
誌謝
中文摘要
1. INTRODUCTION
1.1 Purposes
1.2 Major focuses of this research
1.3 Organization of the dissertation
2. DECISION ANAYSIS UNDER MULTIPLE CRITERIA
2.1 Three major activities for analyzing multiple criteria decision porblems
2.2 Weighting multiple criteria with respect to the goal
2.3 Rating alternatives withrespect to a given citerion
2.4 Composing scores or weihgts
3. ELICITING AWEIGHTING VECTOR FROM THE PAIRWISE COMPARISON MATRIX
3.1 Properties of the pairwise comparison matrix
3.2 Consistency ina pairwise comparison matrix
3.3 Methods for eliciting weights
4. THE RANK REVERSAL PROBLEM AND THE HIERARCHIC COMPOSITION
4.1 The rank reversal problem
4.2 Interpretation of rank reversal
4.3 Distributing problem and grading problem
4.4 Hierarchic composition of a grading problem
5. AN EXAMPLE: SOLID WASTE STUDY
5.1 Evaluation of alternatives
5.2 Setting prioritiesof alternatives
6. CONCLUSION
6.1 Conclusion
6.2 Possible applications of this research
APPENDIX A. ANEXAMPLE OF USING AHP AND A COMPARISON TO MAHP
APPENDIX C. COMPARISON OF THE LEAST SQUARES,THE LOGARITHMIC LEAST SQUARES AND THE EIGENVALUE METHODS IN ESTTMATING RATIOS
APPENDIX D. SOURCE PROGRAM LISTINGS
REFERENCES
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