本論文根據我們所提之非線性規劃法、區間直覺模糊值之餘弦相似度測量、及我們所提之區間直覺模糊值之新的評分函數提出新的多屬性決策方法。我們所提之區間直覺模糊值評分函數可以克服已存在之區間直覺模糊值評分函數之缺點。我們所提之多屬性決策方法可以克服已存在之多屬性決策方法之缺點。首先，我們根據所提之區間直覺模糊值之新的評分函數及決策者所給之決策矩陣計算各個區間直覺模糊值之評分值以建構評分矩陣。然後，我們根據區間直覺模糊值之餘弦相似度測量及各屬性之區間直覺模糊加權值以建構一個非線性規劃模型。然後，我們求解此非線性規劃模型以得到每一個屬性之最佳權重。然後，根據所得之各屬性之最佳權重及所得之評分矩陣，我們計算每一個方案之加權得分。最後，我們根據各方案之加權得分對每一個方案進行排序。如果一個方案之加權得分高於其他方案之加權得分，則此方案具有更佳之偏好排序。我們所提之多屬性決策方法在區間直覺模糊值的環境中提供一個非常有用之方法以作多屬性決策。

In this thesis, we propose a new multiattribute decision making method using the
proposed score function of interval-valued intuitionistic fuzzy values, the cosine
similarity measure of interval-valued intuitionistic fuzzy values, and the proposed
nonlinear programming model. The proposed score function of interval-valued
intuitionistic fuzzy values can overcome the drawbacks of the existing score functions for ranking interval-valued intuitionistic fuzzy values. The proposed multiattribute decision making method can overcome the drawbacks of the existing multiattribute decision making methods based on interval-valued intuitionistic fuzzy values. Firstly, we propose a novel score function of interval-valued intuitionistic fuzzy values to overcome the drawbacks of the existing score functions of interval-valued intuitionistic fuzzy values. Then, we build a score matrix based on the proposed score function of interval-valued intuitionistic fuzzy values and the decision matrix provided by the decision maker. Then, we construct a nonlinear programming model based on the cosine similarity of interval-valued intuitionistic fuzzy values and the interval-valued intuitionistic fuzzy weights of the attributes. Then, we solve the nonlinear programming model to get the optimal weights of the attributes, respectively. Based on the obtained optimal weights of the attributes and the constructed score matrix, we calculate the weighted scores of the alternatives, respectively. Finally, we rank the alternatives based on the obtained weighted scores. The proposed multiattribute decision making method offers us a very useful approach for multiattribute decision making in interval-valued intuitionistic fuzzy
environments.

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