在本論文中，我們提出一個基於機率密度函數及區間直覺模糊評估值的最大區間範圍的變異數及標準差之多屬性決策新方法。首先，我們所提出之多屬性決策方法得到決策者給的決策矩陣中每個區間直覺模糊評估值的最大區間範圍。然後，其計算每個屬性的最大區間範圍的平均值。然後，其得到決策矩陣中出現的每個區間直覺模糊評估值的最大區間範圍的機率密度函數。然後，其計算每個最大區間範圍的變異數並計算每個屬性的最大區間範圍的標準差。然後，其基於所得之決策矩陣中每個區間直覺模糊評估值的最大區間範圍、所得之每個屬性的最大區間範圍的平均值、及所得之每個屬性的最大區間範圍的標準差來構建z分數決策矩陣。然後，其得到每個屬性的區間直覺模糊權重的轉換權重。最後，其根據所得之z分數決策矩陣及每個屬性的區間直覺模糊權重的轉換權重以計算每個選項的加權分數，其中加權分數的值越大，選項的偏好順序越高。本論文所提之多屬性決策新方法可以克服目前已存在之多屬性決策方法的缺點，其在區間直覺模糊環境中提供一種非常有用的多屬性決策方法。

In this thesis, we propose a new multiattribute decision making method based on probability density functions and the variances and standard deviations of the largest ranges of evaluating interval-valued intuitionistic fuzzy values. First, the proposed method obtains the largest range of each evaluating interval-valued intuitionistic fuzzy value in the decision matrix provided by the decision maker. Then, it computes the average value of the largest ranges of each attribute. Then, it obtains the probability density function of the largest range of each evaluating interval-valued intuitionistic fuzzy value appearing in the decision matrix. Then, it computes the variance of each largest range and calculates the standard deviation of the largest ranges of each attribute. Then, it builds the z-score decision matrix based on the obtained largest range of each evaluating interval-valued intuitionistic fuzzy value appearing in the decision matrix, the obtained average value of the largest ranges of each attribute and the obtained standard deviation of the largest ranges of each attribute. Then, it gets the transformed weight of the interval-valued intuitionistic fuzzy weight of each attribute. Finally, it computes the weighted score of each alternative based on the obtained z-score decision matrix and the transformed weight of the interval-valued intuitionistic fuzzy weight of each attribute. The larger the value of the weighted score, the better the preference order of the alternative. The proposed multiattribute decision making method can conquer the shortcomings of the existing multiattribute decision making methods. It provides us with a very useful way for multiattribute decision making in interval-valued intuitionistic fuzzy environments.

S. M. Chen and W. H. Han, “An improved MADM method using interval-valued intuitionistic fuzzy values,” Information Sciences, vol. 467, pp. 489-505, 2018.