根據一般模糊數排序法與區間值模糊數相似度測量法以處理模糊風險分析之新方法

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研究生：	陳進和 Jim-Ho Chen
論文名稱：	根據一般模糊數排序法與區間值模糊數相似度測量法以處理模糊風險分析之新方法 New Methods for Fuzzy Risk Analysis Based on Ranking Generalized Fuzzy Numbers and Similarity Measures between Interval-Valued
指導教授：	陳錫明 Shyi-ming Chen
口試委員:	李惠明 Huey-Ming Lee 呂永和 Yung-Ho Lu 蕭瑛東 Ying-Tung Hsiao 沈榮麟 Victor R.L. Shen
學位類別：	碩士 Master
系所名稱：	電資學院 - 資訊工程系 Department of Computer Science and Information Engineering
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	99
中文關鍵詞：	模糊風險分析、一般化模糊數、相似度測量、區間值模糊數
外文關鍵詞：	fuzzy risk analysis, generalized fuzzy numbers, similarity measures, interval-valued fuzzy numbers
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在本論文中，針對模糊風險分析我們提出兩種方法，一是基於排序一般模糊數，另一則是區間值模糊數相似度測量法。首先，我們針對排序一般模糊數提出一個新方法以處理模糊風險分析問題。本方法考慮了一般模糊數的解模糊值、權重以及擴張度。再者，我們應用此方法排序一般模糊數以提出一個新方法去處理模糊風險分析問題。接下來，我們針對區間值模糊數提出一個新的相似度測量方法。本方法考慮了區間值模糊數的五項因素，包括了區間值模糊數的上模糊數之間，其X軸的相似度、區間值模糊數的上模糊數之間，其權重的相似度、區間值模糊數的上模糊數之間，其擴張度的相似度、區間值模糊數之間，其X軸的相似度、區間值模糊數之間，其Y軸的相似度。除此之外，我們也提出新的區間值模糊數運算子，並且將我們提出的相似度測量方法應用於基於區間值模糊數的風險分析問題上。本論文所提出的風險分析方法提供良好的方式以處理模糊數風險分析問題。

In this thesis, we present two methods for fuzzy risk analysis based on ranking generalized fuzzy numbers and similarity measures between interval-valued fuzzy numbers. First, we present a new method for ranking generalized fuzzy numbers for handling fuzzy risk analysis problems. The proposed method considers defuzzified values, the weight and the spreads of generalized fuzzy numbers. Moreover, we also apply the proposed method for ranking generalized fuzzy numbers to present a new method for dealing with fuzzy risk analysis problems. Then, we present a new similarity measure for interval-valued fuzzy numbers. The proposed similarity measure considers five factors, i.e., the degree of similarity on X-axis between the upper fuzzy numbers of the interval-valued fuzzy numbers, the degree of similarity about the weight of the upper fuzzy numbers of the interval-valued fuzzy numbers, the spread between the upper fuzzy numbers of the interval-valued fuzzy numbers, the degree of similarity on the X-axis between the interval-valued fuzzy numbers, and the degree of similarity on the Y-axis between the interval-valued fuzzy numbers. Moreover, we also present new interval-valued fuzzy numbers arithmetic operators and apply the proposed similarity measure to present a new method for dealing with fuzzy risk analysis problems based on interval-valued fuzzy numbers. The proposed fuzzy risk analysis methods provide us a useful way for handling fuzzy risk analysis problems.

Abstract in Chinese…………………………………………………………… i
Abstract in English…………………………………………………………… iii
Acknowledgements………………………………………………………………  iv
Contents…………………………………………………………………………  v
List of Figures and Tables…………………………………………………  viii
Chapter 1  Introduction……………………………………………………… 1
1  Motivation………………………………………………………………… 1
2  Organization of This Thesis…………………………………………  2
Chapter 2  Preliminaries……………………………………………………  4
1  Generalized Fuzzy Numbers……………………………………………  4
2  Type-1 Fuzzy NumberArithmetic Operations………………………… 4
3  Interval-Valued Fuzzy Numbers………………………………………  5
4  Some Existing Methods for Ranking Fuzzy Numbers………………  6
4.1  Yager’s Centroid-Index Method…………………………………  6
4.2  Chen’s Defuzzifing Index Method………………………………  6
4.3  Cheng’s Coefficient of Variation Index Method……………  7
4.4  Chu-and-Tsao’s Score Function Method………………………… 8
4.5  Chen-and-Chen’s Fuzzy Ranking Method………………………   8
4.6  Chen-and-Chen’s Fuzzy Ranking Method……………………    10
4.7  Deng-and-Liu’s Centroid-Index Method………………………  11
4.8  Chen-and-Chen’s Fuzzy Ranking Method……………………    12
5  Some Existing Similarity Measures………………………………   13
5.1  Chen’s Similarity Measure……………………………………   13
5.2  Lee’s Similarity Measure……………………………………    14
5.3  Hsieh and Chen’s Similarity Measure………………………   14
6  A Similarity Measure between Interval-Valued Fuzzy Numbers…15
7 The Standard Deviations and The Centers-of-Gravity of Fuzzy Numbers………………………………………                            17
8  Summary…………………………………………………………         18
Chapter 3  A New Methods for Ranking Generalized Fuzzy Numbers… 19
1  A Method for Ranking Generalized Fuzzy Numbers…………………19
2  A Comparison of the Ranking Results of the Fuzzy Ranking   Method with the Existing Methods……………………………………                     22
3  Summary…………………………………………………………         28
Chapter 4  Handling Fuzzy Risk Analysis Problems Based on the Proposed Fuzzy Ranking Method…………………………………………………             29
Chapter 5  Similarity Measure between  Interval-Valued Fuzzy Numbers 36
1  A New Similarity Measure between Interval-Valued Fuzzy Numbers 36
2  Experimental Results of Similarity Measure between Interval-Valued    Fuzzy Numbers………………………………………………                      51
3  Summary…………………………………………………………         54
Chapter 6  Interval-Valued Fuzzy Number Arithmetic Operations……55
1  The Existing Interval-Valued Fuzzy Number Arithmetic Operations… 55
2  New Interval-Valued Fuzzy Number Arithmetic Operations………58
3  The Properties of the Proposed Interval-Valued Fuzzy Number Arithmetic Operations………………………………………………                   65
4  Summary……………………………………………………………       84
Chapter 7  Fuzzy Risk Analysis Based on the Proposed Similarity Measure… 85
Chapter 8  Conclusions…………………………………………………………… 94
1  Contributions of This Thesis……………………………………    94
2  Future Researches…………………………………………………     95
References……………………………………………………………………… 96

                                

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