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研究生:陳新元
研究生(外文):Hsin-Yuan Chen
論文名稱:倒數矩陣上決策評估的容忍度分析
論文名稱(外文):Tolerance Analysis on a Positive Reciprocal Matrix of Evaluation Decisions
指導教授:王小璠王小璠引用關係
指導教授(外文):Hsiao-Fan Wang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:工業工程與工程管理學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:50
中文關鍵詞:容忍度分析固有系統成對倒數矩陣可接受的一致性有效度
外文關鍵詞:Tolerance AnalysisEigensystemPositive Reciprocal MatrixAcceptable ConsistencyEffectiveness
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矩陣上的容忍度分析是十分的複雜,然而近幾年來卻是廣泛的討論,特別是在決策評估的成對倒數矩陣(positive reciprocal matrix)上。成對倒數矩陣的容忍度分析是在固有系統中,隨著一致性和倒數性質的要求下所執行的。在矩陣和可被視為在評估問題中屬性重要性權重的固有向量之間的關係,透露了在容忍度分析中高度的複雜性卻有趣的含意。因此,我們所提出容忍度分析的第一個主題是給定一個成對倒數矩陣和所導致的權重向量,在可接受的一致性要求下,對於這一個權重向量而言,成對倒數矩陣最大的容忍範圍為何?既然在給定成對倒數矩陣上的容忍度分析中,同一個權重向量未必是有意義的,因此,我們的第二個主題是給定一個一致性的成對倒數矩陣,在要求達到有效度的前提下,成對比較矩陣的最大容忍範圍為何?在得到容忍範圍之後,我們進一步提出了可能的應用。從給定有效的容忍範圍,以建構在固有系統中同一或不同權重的一致性成對倒數矩陣。我們將以例子來驗證所提出的步驟。結果顯示了容忍度分析提供充分的資訊給決策者做一個較佳的決策。
The tolerance analysis on a matrix is highly complicated and has been widely discussed in recent years, especially on a positive reciprocal matrix (PRM) for an evaluation decision. With the requirement of the consistency and reciprocal, tolerance analysis of a PRM can be performed in an eigensystem. The relation between the matrix and the resultant eigenvector that can be regarded as weights of importance of the attributes in an evaluation problem reveals the high complexity yet interesting interpretation in tolerance analysis. Therefore, the 1st issue of our tolerance analysis is given a PRM and the resultant weighting vector, what is the largest tolerance levels of PRM with respective to the vector under the acceptable consistent requirement? Since tolerance analysis on a given PRM is not necessarily significant in relation to the weighting vector, therefore our 2nd issue is given a consistent PRM, what would be the largest tolerance levels such that the required effectiveness will be obtained. After the tolerance levels are acquired, we further propose the possible applications for constructing a consistent PRM with/without the same weight in an eigensystem from the given effective tolerance levels. The procedure has been demonstrated by an illustrative example. The result shows that the tolerance analysis provides the sufficient information to make a better decision.
CONTENTS
ABSTRACT I
CHINESE ABSTRACT II
ACKNOWLEDGEMENT III
CONTENTS IV
FIGURE AND TABLE CAPTIONS VI
CHAPTER 1. INTRODUCTION 1
CHAPTER 2. LITERATURE REVIEW 5
2.1 Basic Concept and Definitions 6
2.2 Calibration Methods of An Inconsistent Matrix 8
2.3 Calibration Effectiveness 9
2.4 Interval Computation 10
2.5 Summary 11
CHAPTER 3. TOLERANCE ANALYSIS OF A PRM BY CONSISTENCY CONDITION 12
3.1 Tolerance Analysis in an Eigensystem 12
3.1.1 Interval Derivation 12
3.1.2 Construction of a New PRM with the Same Eigenvector 15
3.1.3 Construction of a New PRM with Different Eigenvector 15
3.2 Procedure of Tolerance Analysis and Reconstruction of An Inconsistent PRM 19
3.3 Numerical Example 21
3.4 Summary 22
CHAPTER 4. TOLERANCE ANALYSIS OF A CONSISTENT PRM BY EFFECTIVENESS CONDITIONS 24
4.1 Tolerance Analysis with Single Parameter 25
4.1.1 Theoretical Development 25
4.1.2 Pattern of the Tolerance Matrix 26
4.1.3 The Procedure 28
4.1.4 Numerical Example 29
4.2 Tolerance Analysis with Different Parameters 32
4.2.1 The Procedure 32
4.2.2 Numerical Example 33
4.3 Summary 35
CHAPTER 5. AN ILLUSTRATIVE CASE 39
5.1 A Numerical Example For Tolerance Analysis 39
5.2 A Numerical Example of Effectiveness For Tolerance Analysis 41
5.2.1 Tolerance Analysis For The Same Variation 41
5.2.2 Tolerance Analysis For The Different Variations 44
5.3 Summary 46
CHAPTER 6. SUMMARY AND CONCLUSION 49
REFERENCE 50

FIGURE AND TABLE CAPTIONS
Figure 4.1 Range of “a” 26
Figure 4.2 Flow Chart of the Algorithm (1) 37
Figure 4.3 Flow Chart of the Algorithm (2) 38

Table3.1 THE MEAN CONSISTENCY INDEX OF RANDOMLY GENERATED
MATRICES 20
REFERENCE
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2.Hillier F.S., Lieberman G.J., Introduction to Operations
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3.Kwiesielewicz M., Uden, E.V., Inconsistent and
contradictory judgements in pairwise comparison method in
the AHP, Computers & Operations Research 31 (2004) 713-719
4.Ma. Weiyi, X. Jiangyue, W. Yixiang, A practical approach
to modifying pairwise comparison matrices and two
criteria of modificatory effectiveness, Systems Science
and Systems Engineering 2 (1993) 334-338
5.Moore R.E., Interval Analysis, Prentice-hall, N.J., 1966
6.Moore R.E., Methods And Application of Interval Analysis,
SIAM, Philadelphia,1979
7.Saaty T.L., The Analytic Hierarchy Process, McGraw-Hill,
New York, 1980
8.Wilkinson J.H., The Algebraic Eigenvalue Problem, Oxford
University Press, London, 1965
9.Xu Zeshui, Wei Cuiping, A consistency improving method in
the analytic hierarchy process, European Journal of
Operational Research 116 (1999) 443-449
10.Xu Z., On consistency of the weighted geometric mean
complex judgment matrix in AHP, European Journal of
Operational Research 126 (2000) 683-687
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