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研究生:張文貴
研究生(外文):Chang, Wen-Kui
論文名稱:乏確方案之比序方法及其在決策分析上應用之研究
論文名稱(外文):A Study on the Ranking of Fueey Alternatives and Its Application to Decision Making
指導教授:趙榮耀趙榮耀引用關係張系國張系國引用關係
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:1982
畢業學年度:70
語文別:中文
論文頁數:175
中文關鍵詞:集合理論方案
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本論文主要目的在探討乏確集合理論 (fuzzy sets theory) 應用在決策分析之可行性。首先,以推廣定理 (extension principle) 為基礎,導衍出一套易於操作之運算法則,專門處理由凸狀乏確數 (convexfuzzy numbers) 形成之水準集合 (level sets); 此等法則對於語言變數 (linguistic variables) 之計算甚為方便而且有效。
透過水準集合之理念,本文提出一個方法以比較各種乏確方案 (fuzzy alternatives) 之優劣,并應用到兩種不同型態之方案策略:一種用不連續的乏確數 (discrete fuzzy numbers) 表示,另一種由完全凸狀的乏確數 (strictly convex fuzzy numbers) 描述;同時本文也舉出後者的五種不同情況加以比較,結果顯示本文之方法較其他四個方法更佳。
藉看上述之推廣運算法則及乏確方案之比序方法,作者導出一個方術(algorithm) 以解決雙支點之語言決策樹的問題 (binary linguistic decision tree);其好處在於吾人不必花很多時間及精力去求取數據的精確度。因此,對於一些無法精確描述或難以嚴密定義的複雜系統,它的確是一種近似卻非常實際的處理方法。
最後該方術被應用到幾個不同之實際個案,所有結果皆與不用乏確集合理論之傳統方法 (conventional approach) 導出者完全吻合。由此可見,本論文提出之方術,不但未與傳統方法衝突,而且更適合於處理傳統方法不易(甚或無法)處理的人文系統 (humanistic systems)。
The feasibility of the application of fuzzy sets theory to decision making is investigated in this research. The arithmetic operations on level sets of convex fuzzy numbers are studied in detail, on the basis of the extension principle which was introduced by Professor L. A. zadeh in 1975. It is shown that these operations are convenient and efficient in the computation of linguistic variables.
By means of the concept of level sets, a new method to rank various fuzzy alternatives is presented. The presented method is then applied to two kinds of fuzzy numbers, one is discrete fuzzy numbers and the other is strictly convex fuzzy numbers. Five illustrations for the latter are shown, which imply that the capability of the proposed method is much more improved than those which have been published in the literature.
Through the extended operations on linguistic variables as well as linguistic hedges, an algorithm is proposed to evaluate a binary linguistic decision tree. The advantage of the linguistic decision tree is to relax the necessity for the determination of the precise numbers and thus this linguistic approach is considered an approximate and yet practical means to describe the behavior of systems, which are either too complex or too ill-defined to give an exact description.
Several case studies are illustrated to employ the proposed algorithm. Bayesian analysis to a binary decision tree is also presented. The results are shown to be in good agreement with those in the conventional case.
TABLE OF CONTENTS
ACKNOWLEDGEMENT
ABSTRACT
LIST OF FIGURES
LIST OF TABLES
CHAPTER 1. INTRODUCTION
1.1 Precision and Fuzziness
1.2 Argument in Fuzzy Sets Theory
1.3 Perspective of Fuzzy sets Theory
1.4 Motivation of This Research
1.5 Outlines of This Paper
CHAPTER 2. THEORETICAL BACKGROUND OF FUZZUY SETS THEORY
2.1 Introduction
2.2 notation and terminology
2.3 Set-Theoretic Operations
2.4 Convex Fuzzy Numbers
2.5 Level Sets of a Fuzzy Number
2.6 The Extension Principle and Some Derived Results
CHAPTER 3. ANALYSIS OF A LINGUISTIC APPROXIMATION
3.1 Introduction
3.2 Linguistic Variables
3.3 Interpretation of Linguistic Hedges
3.4 Formulation of some linguistic Conepts
CHAPTER 4. DECISION MAKING UNDER FUZZINESS
4.1 Introduction
4.2 FuzzyRating of Multi-Criteria Alternatives
4.3 Review of Ranking between Fuzzy Alternatives
4.4 The Proposed Method of Ranking by Level Sets
4.5 Ranking of Discrete Fuzzy Numbers
4.6 Ranking of Strictly Convex Fuzzy Numbers
4.7 Comparsion under Triangular Membership Functions
CHAPTER5. EVALUATION OF LINGUISTIC DECISION TREES
5.1 Introduction
5.2 Conventional Decision Trees
5.3 Computation with Linguistic Probabilities
5.4 Fuzzy Decision Trees
5.5 Linguistic Expectation at Chance Forks
5.6 Summary of the Proposed Algorithm
CHAPTER 6. EXPERIMENTAL STUDIES
6.1 Introduction
6.2 Tolerance Analsis using Fuzzy Sets
6.3 A Simple Decision Problem
6.4 A Binary Linguistic Decision Tree
6.5 Bayesian Analysis of A Binary Fuzzy Decision Problem
CHAPTER 7. CONCLUSION AND DISCUSSION
7.1 Introduction
7.2 Summary
7.3 Possible Applications and Remarks
7.4 Recommendations for Future Work
APPENDIX
LIST OF REFERENCES
中文摘要
研究生個人資料
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