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Author: 徐明漢
Ming-Han Hsu
Thesis Title: 根據區間直覺模糊值之得分函數、分數矩陣、及非線性規劃法以作多屬性決策之新方法
Multiple Attribute Decision Making Using Novel Score Function of Interval-Valued Intuitionistic Fuzzy Values, Score Matrix, and Nonlinear Programming Model
Advisor: 陳錫明
Shyi-Ming Chen
Committee: 呂永和
Yung-Ho Leu
程守雄
Shou-Hsiung Cheng
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: 83
Keywords (in Chinese): 決策矩陣區間直覺模糊值多屬性決策偏好順序得分函數分數矩陣
Keywords (in other languages): Decision Matrix, Interval-Valued Intuitionistic Fuzzy Value, Multiple Attribute Decision Making, Preference Order, Score Function, Score Matrix
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  • 本論文旨在根據我們所提之區間直覺模糊值之得分函數、分數矩陣、及我們所提之非線性規劃法提出一個新的多屬性決策方法。首先,我們根據所提之新的得分函數以計算決策矩陣中之每一個區間直覺模糊值之得分值來建構分數矩陣,其中我們所提之區間直覺模糊值之新的得分函數能夠克服目前已存在之區間直覺模糊值得分函數的缺點。然後,我們分別計算在分數矩陣中每一行得分值之平均值。然後,我們根據所得之分數矩陣、在分數矩陣中每一行得分值之平均值、偏差變量的概念、及決策者所提供之每一個屬性的區間直覺模糊權重來構建非線性規劃模型。然後,我們求解非線性規劃模型以獲得每一個屬性的最佳權重。最後,我們根據所得之分數矩陣及每一個屬性的最佳權重計算每一個方案的加權分數,且根據所得之每一個方案的加權分數對每一個方案進行排序,其中加權分數越大的方案,其偏好順序越好。我們所提之多屬性決策方法能夠克服目前已存在之多屬性決策方法的缺點。我們所提之多屬性決策方法提供一個很有用的方法以在區間直覺模糊環境下作多屬性決策。


    In this thesis, we propose a new multiple attribute decision making method on the basis of the proposed score function of interval-valued intuitionistic fuzzy values, the score matrix, and the proposed nonlinear programming model. Firstly, we apply the proposed score function of interval-valued intuitionistic fuzzy values to build the score matrix, where the proposed score function of interval-valued intuitionistic fuzzy values can conquer the shortcomings of the existing score functions of interval-valued intuitionistic fuzzy values. Then, we compute the average value of the values appeared at each column of the score matrix. Then, we construct the nonlinear programming model based on the obtained score matrix, the obtained average value of the values appeared at each column of the score matrix, the concept of deviation variables, and the interval-valued intuitionistic fuzzy weight of each attribute offered by the decision maker. Then, we solve the nonlinear programming model to obtain the optimal weight of each attribute. Then, we compute the weighted score of each alternative using the obtained score matrix and the optimal weights of the attributes. Finally, the alternatives are ranked according to the obtained weighted scores. The larger the weighted score of an alternative, the better the preference order of the alternative. The proposed multiple attribute decision making method can overcome the drawbacks of the existing multiple attribute decision making methods. It offers us a very useful way for multiple attribute decision making in interval-valued intuitionistic fuzzy environments.

    ABSTRACT ii Acknowledgements iii Contents iv Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Organization of This Thesis 4 Chapter 2 Preliminaries 5 2.1 Interval-Valued Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Values 5 2.2 Standard Scores 6 2.3 Score Functions of Interval-Valued Intuitionistic Fuzzy Values 6 2.4 Ranking Method of Interval-Valued Intuitionistic Fuzzy Values 7 2.5 Summary 7 Chapter 3 Multiple Attribute Decision Making Based on Score Function of Interval-Valued Intuitionistic Fuzzy Values and the Means and the Variances of Score Matrices 8 3.1 Chen and Tsai’s Multiple Attribute Decision Making Method 8 3.2 Drawbacks of Chen and Tsai’s Multiple Attribute Decision Making Method 10 3.3 Summary 26 Chapter 4 The Proposed Score Function of Interval-Valued Intuitionistic Fuzzy Values 27 4.1 A Novel Score Function 27 4.2 Properties of the Proposed Score Function 27 4.3 A Comparison of the Existing Score functions 28 4.4 Summary 36 Chapter 5 Multiple Attribute Decision Making Method Based on the Proposed Score Function of Interval-Valued Intuitionistic Fuzzy Values, the Score Matrix, and the Proposed Nonlinear Programming Model 37 5.1 A New Multiple Attribute Decision Making Method 37 5.2 Application Examples 39 5.3 Summary 66 Chapter 6 Conclusions 67 6.1 Contributions of This Thesis 67 6.2 Future Research 67 References 69

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