臺灣博碩士論文加值系統

根據直覺模糊集合以作多準則決策是一個重要的研究課題。近年來，已有一些根據直覺模糊集合以作多準則決策之方法被提出。在本論文中，首先我們提出一個根據直角三角模糊數的中心點的轉換技術以測量直覺模糊集合之相似度的新方法並且證明其符合相似度測量的特性。然後，我們提出一個根據TOPSIS法及直覺模糊集合之相似度測量以作模糊多準則決策之新方法，其能夠解決已存在之方法在某些情況下由於除以零而不能得到方案間之偏好排序的缺點。最後，我們用一些例子以說明我們所提之新的多準則決策方法可以克服已存在之方法的缺點。我們所提之方法提供我們一個有用的方法以根據直覺模糊集合以作模糊多準則決策問題。

Multicriteria decision making based on intuitionistic fuzzy sets is an important research topic. In recent years, some methods have been presented for multicriteria decision making based on intuitionistic fuzzy sets. In this thesis, we propose a new similarity measure between intuitionistic fuzzy sets based on the centroid points of the transformed right-angled triangular fuzzy numbers and prove some properties of the proposed similarity measure between intuitionistic fuzzy values. Then, we propose a new multicriteria decision making method based on the TOPSIS method and the proposed similarity measure between intuitionistic fuzzy sets to overcome the drawbacks of the existing methods, where the existing methods have the drawbacks that they cannot get the preference order of alternatives in some situations due to the fact that they have “the division by zero problem”. We also use some examples to illustrate the proposed multicriteria decision making method can overcome the drawbacks of the existing methods. The proposed multicriteria decision making method provides us with a useful way for multicriteria decision making in intuitionistic fuzzy environments.

Abstrct in Chinese.........................................................i
Abstrct in English........................................................ii
Acknowledgements.........................................................iii
Contents..................................................................iv
List of Figures and Tables................................................vi
Chapter 1 Introduction.....................................................1
1.1 Motivation............................................................1
1.2 Related Literature....................................................2
1.3 Organization of This Thesis...........................................7
Chapter 2 Preliminaries....................................................8
2.1 Intuitionistic Fuzzy Sets.............................................8
2.2 Properties of Similarity Measures Between Intuitionistic Fuzzy Sets ...........................................................................9
2.3 Summary...............................................................9
Chapter 3 A Review of Existing Methods for Fuzzy Multicriteria Decision Making Based on Intuitionistic Fuzzy Sets.................................10
3.1 Joshi and Kumar’s Method.............................................10
3.2 Wang and Wei’s Method................................................13
3.3 Wu and Chen’s Method.................................................15
3.3 Summary..............................................................20
Chapter 4 A Novel Similarity Measure Between Intuitionistic Fuzzy Sets...21
4.1 A Review of Existing Similarity Measures Between Intuitionistic Fuzzy Sets......................................................................21
4.2 A New Similarity Measure Between Intuitionistic Fuzzy Sets............33
4.3 Pattern Recognition Applications......................................52
4.4 Summary...............................................................61
Chapter 5 A New Method for Multicriteria Decision Making Based on TOPSIS Method and the Proposed Similarity Measure Between Intuitionistic Fuzzy Sets ..........................................................................62
5.1 A New Multicriteria Decision Making Method Based on the TOPSIS Method and the Proposed Similarity Measure Between Intuitionistic Fuzzy Sets.....62
5.2 Application Examples..................................................65
5.3 Summary..............................................................122
Chapter 6 Conclusions....................................................123
6.1 Contributions of This Thesis.........................................123
6.2 Future Research......................................................123
References...............................................................125

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