臺灣博碩士論文加值系統

近幾年來，模糊數的相似度測量在模糊決策 、資訊融合和模糊風險分析之中扮演了重要的角色。在本論文中，我們提出了可應用在一般模糊數以及區間值模糊數的兩個相似度測量方法，此兩種方法考慮了模糊數的幾何距離、周長、高度及重心。之外，我們也提出區間值模糊數之調整演算法。根據我們所提之一般模糊數相似度測量方法及區間值模糊數相似度測量方法，我們分別提出新的風險分析方法，我們所提的風險分析方法可以克服目前已存在之方法的缺點。他們比目前已存在之方法更具智慧及更具有彈性的作風險分析。

In recent years, the task of measuring the degree of similarity between fuzzy numbers plays an important role in fuzzy decision making, information fusion and fuzzy risk analysis. In this thesis, we present two similarity measures for generalized fuzzy numbers and interval-valued fuzzy numbers. It combines the concepts of geometric distance, the perimeter, height and center of gravity point of generalized fuzzy numbers and interval-valued fuzzy number, respectively. Moreover, we also presented an interval-valued fuzzy number adjusting algorithm. Based on proposed similarity measures, we propose two new methods for handling fuzzy risk analysis problems. The proposed fuzzy risk analysis methods can overcome the drawback of existing methods. They can deal with fuzzy risk analysis in a more intelligent and flexible manner.

Abstract in Chinese………………………………………………………………… i
Abstract in English………………………………………………………………… ii
Acknowledgements………………………………………………………………… iii
Contents…………………………………………………………………………… iv
List of Tables………………………………………………………………………… vi
List of Tables……………………………………………………………………… vii
Chapter 1 Introduction…………………………………………………………… 1
1.1 Motivation…………………………………………………………… 1
1.2 Organization of This Dissertation….………………………………… 1
Chapter 2 Literatures Review………………………..…………...…………… 3
2.1 Fuzzy Sets Theory…………………………………………………… 3
2.2 Fuzzy Numbers and Their Arithmetic Operations………………… 4
2.3 Generalized Fuzzy Numbers and Their Arithmetic Operations……… 6
2.4 Interval-Valued Fuzzy Numbers and Their Arithmetic Operations…… 8
2.5 Summary…………….……………………………………………… 11
Chapter 3 A New Method to Calculate the Degree of Similarity between Generalized Fuzzy Numbers….…………………………………… 12
3.1 Chen’s Similarity Measure……………………………………….… 13
3.2 Hsieh-and-Chen’s Similarity Measure……………………………… 13
3.3 Lee’s Similarity Measure…………………………………………… 14
3.4 Chen-and-Chen’s Similarity Measure……………………………… 15
3.5 A New Similarity Measure between Generalized Fuzzy Numbers…… 17
3.6 A Comparison of the Similarity Measures………………………… 22
3.7 Summary………………………………….……………………...…… 26
Chapter 4 A New Approach for Fuzzy Risk Analysis Based on Similarity Measures of Generalized Fuzzy Numbers………………………… 27
4.1 New Division Operation for Fuzzy Risk Analysis………………… 27
4.2 Fuzzy Risk Analysis Based on the Proposed Similarity Measure of Generalized Fuzzy Numbers……………………………………… 28
4.3 Summary……………………………………………………………. 37
Chapter 5 A New Method to Calculate the Degree of Similarity between Interval-Valued Fuzzy Numbers…………………………………… 38
5.1 A Review of Existing Similarity Measures between Interval-Valued Fuzzy Numbers……………………………………………………… 38
5.2 A New Similarity Measure between Interval-Valued Trapezoidal Fuzzy Numbers……………………………………………………………… 40
5.3 A Comparison of the Similarity Measures between Interval-Valued Trapezoidal Fuzzy Numbers………………………………………… 55
5.4 Summary……………………………………………………………… 60
Chapter 6 A New Approach for Fuzzy Risk Analysis Based on Similarity Measures of Interval-Valued Fuzzy Number……………………… 61
6.1 New Division Operation for Interval-Valued Fuzzy Numbers……… 61
6.2 Interval-Valued Fuzzy Number Adjustment Algorithm……………… 62
6.3 Fuzzy Risk Analysis Based on The Proposed Similarity Measure between Interval-Valued Fuzzy Numbers…………………………… 69
6.4 Summary……………………………………………………………… 79
Chapter 7 Conclusions…………………………………………………………… 80
7.1 Contributions of This Thesis………….……………………………… 80
7.2 Future Research..………………………….………………………… 80
References……………………………………………………………………..……… 81

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