在本論文中，我們提出根據區間直覺模糊值、區間直覺模糊加權算術平均運算子、及非線性規劃法以作模糊多屬性決策之新方法。首先，我們根據以區間直覺模糊值表示之屬性的權重計算出其最大之權重範圍，並調整不合理的最大權重範圍。然後，我們根據區間直覺模糊值之得分函數及決策者所提供之決策矩陣得到一個轉換決策矩陣。然後，我們根據此轉換決策矩陣及屬性之權重的最大範圍建立一個非線性規劃模型。然後，我們利用所建立的非線性規劃模型求出各屬性的最佳權重。然後，我們利用決策矩陣、各屬性的最佳權重、及區間直覺模糊加權算術平均子以得到每個方案的區間直覺模糊加權平均值。最後，我們根據得分函數、精確函數、歸屬值不確定指數、及猶豫值不確定指數以得到每個方案的排序。本論文所提的模糊多屬性決策之新方法可以克服目前已存在的方法之缺點，其提供我們一個在區間直覺模糊的環境下非常有用的模糊多屬性決策方法。

In this thesis, we propose a new fuzzy multiattribute decision making method based on interval-valued intuitionistic fuzzy values, the interval-valued intuitionistic fuzzy weighted averaging operator, and the nonlinear programming methodology. Firstly, the proposed method calculates the largest ranges of interval-valued intuitionistic fuzzy weights of attributes and modifies unreasonable ranges of interval-valued intuitionistic fuzzy weights. Then, it gets the transformed decision matrix based on the score function of interval-valued intuitionistic fuzzy values and the decision matrix provided by the decision maker. Then, it constructs the nonlinear programming model based on the obtained transformed decision matrix and the obtained largest ranges of interval-valued intuitionistic fuzzy weights of attributes. Then, it gets the optimal weights of the attributes based on the obtained nonlinear programming model. Then, it calculates the weighted evaluating interval-valued intuitionistic fuzzy values of the alternatives based on the decision matrix, the obtained optimal weights of the attributes and the interval-valued intuitionistic fuzzy weighted averaging operator. Finally, it gets the preference order of the alternatives based on the score function, the accuracy function, the membership uncertainty index and the hesitation uncertainty index of interval-valued intuitionistic fuzzy values. The proposed fuzzy multiattribute decision making method can overcome the drawback of the existing methods. It provides us with a very useful way for fuzzy multiattribute decision making in interval-valued intuitionistic fuzzy environments.

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