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Author: 黃紹恩
Shao-En Huang
Thesis Title: 根據非線性規劃、區間直覺模糊值之新的得分函數、及得分值之離散程度以作多屬性決策之新方法
Multiattribute Decision Making Using Nonlinear Programming Methodology, Score Function of Interval-Valued Intuitionistic Fuzzy Values, and the Dispersion Degree of Score Values
Advisor: 陳錫明
Shyi-Ming Chen
Committee: 程守雄
Shou-Hsiung Cheng
呂永和
Yung-Ho Leu
Degree: 碩士
Master
Department: 電資學院 - 資訊工程系
Department of Computer Science and Information Engineering
Thesis Publication Year: 2023
Graduation Academic Year: 111
Language: 英文
Pages: 85
Keywords (in Chinese): 決策矩陣區間直覺模糊值多屬性決策偏好排序得分函數分數矩陣
Keywords (in other languages): Decision Matrix, Interval-Valued Intuitionistic Fuzzy Value, Multiattribute Decision Making, Preference Order, Score Function, Score Matrix
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本論文旨在根據我們所提之非線性規劃法、我們所提之區間直覺模糊值之得分函數、及在得分矩陣中每一行中之得分值的離散程度提出一個新的多屬性決策方法。首先,我們提出一個新的區間直覺模糊值之得分函數以建構分數矩陣。我們所提之區間直覺模糊值之得分函數能夠克服目前已存在之區間直覺模糊值之得分函數的方法之缺點。然後,我們計算在分數矩陣中每一行中的得分值之離散程度。然後,我們根據所得到之分數矩陣、在得分矩陣中每一行中之得分值的離散程度、及決策者所給之每一個屬性之區間直覺模糊加權值建構一個非線性規劃模型以得到每一個屬性之最佳權重。然後,我們根據所得之分數矩陣及所得之每一個屬性之最佳權重計算每一個方案之加權分數。最後,我們根據所得之每一個方案之加權分數以得到每一個方案的偏好順序。我們所提之多屬性決策方法能夠在區間直覺模糊的環境中克服目前已存在之多屬性決策方法的缺點。


In this thesis, we propose a new multiattribute decision making method based on the proposed nonlinear programming model, the proposed score function of interval-valued intuitionistic fuzzy values, and the dispersion degree of the score values appeared in each column of the score matrix. Firstly, we propose a new score function of interval-valued intuitionistic fuzzy values to build the score matrix. The proposed score function of interval-valued intuitionistic fuzzy values can overcome the shortcomings of the existing score functions of interval-valued intuitionistic fuzzy values. Then, we compute the dispersion degree of the score values appeared at each column of the score matrix. Then, we construct a nonlinear programming model to obtain the optimal weight of each attribute based on the obtained score matrix, the dispersion degree of the score values appeared at each column of the score matrix, and the interval-valued intuitionistic fuzzy weights of the attributes provided by the decision maker. Then, we compute the weighted score of each alternative based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, we obtain the preference order of the alternatives based on the obtained weighted scores of the alternatives. The proposed multiattribute decision making method can overcome the drawbacks of the existing multiattribute decision making methods in interval-valued intuitionistic fuzzy environments.

Abstract in Chinese i Abstract in English ii Acknowledgements iii Contents iv Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Organization of This Thesis 2 Chapter 2 Preliminaries 4 2.1 Interval-Valued Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Values 4 2.2 Largest range of Interval-Valued Intuitionistic Fuzzy Values 4 2.3 Score Functions of Interval-Valued Intuitionistic Fuzzy Values 5 2.4 Standard Scores 7 2.5 Ranking Method of Interval-Valued Intuitionistic Fuzzy Values 7 2.6 Dispersion Degree of Score Values 7 2.7 Summary 8 Chapter 3 A Novel Score Function of Interval-Valued Intuitionistic Fuzzy Values 9 3.1 A Novel Score Function 9 3.2 Properties of the Proposed Score Function 9 3.3 Comparison with Some Existing Score functions 10 3.4 Summary 26 Chapter 4 Analyze the Shortcomings of Chen and Tsai’s Multiattribute Decision Making Method 27 4.1 Chen and Tsai’s Multiattribute Decision making Method 27 4.2 Drawbacks of Chen and Tsai’s Multiattribute Decision Making Method 28 4.3 Summary 43 Chapter 5 Multiattribute Decision Making Based on Nonlinear Programming Methodology, Score Function of Interval-Valued Intuitionistic Fuzzy Values, and the Dispersion Degree of Score Values 45 5.1 A New Multiattribute Decision Making Method 45 5.2 Application Examples 47 5.3 Summary 69 Chapter 6 Conclusions 70 6.1 Contributions of This Thesis 70 6.2 Future Research 70 References 71

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