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題名：泰勒近似法於灰色預測及其在教育資訊與測驗統計之應用
作者：阮福海
作者(外文)：Nguyen Phuoc Hai
校院名稱：國立臺中教育大學
系所名稱：教育資訊與測驗統計研究所
指導教授：許天維
永井正武
學位類別：博士
出版日期：2015
主題關鍵詞：泰勒近似方法；灰色預測；灰色系統理論；教育資訊與測驗統計；灰關聯分析；接收者操作特徵；MATLAB工具箱；Taylor approximation method；Grey prediction；Grey system theory；Educational information and measurement；GRA；ROC；MATLAB toolbox
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本研究提出泰勒近似法於灰色預測及其在教育資訊與測驗統計之應用，泰勒近似法於灰色預測是結合泰勒近似方法與灰色預測在灰色系統理論發展而成的研究方法。灰色系統理論 (Grey System Theory) 為鄧聚龍於 1982 年所提出。近年來，灰色系統理論已成功地用於各種預測的應用。它已成為解決離散數據，不完整信息與不確定性問題的一種非常有效的方法。在教育資訊與測驗統計中當系統的數據以傳統統計方法不能夠有效的計算時，應用灰色系統理論可以得到良好的結果，其中灰色預測模型對預測的問題具有非常重要的功能。然而，應用灰色預測模型仍存在一個問題就是預測的準確性還不夠令人滿意。因灰色系統理論之灰色預測精度係數仍不是最佳係數，故使用泰勒近似法於灰色預測可以通過多次近似計算，得到預測的最優價值。本研究所採用的研究方法包涵理論分析與實證研究跟泰勒近似法於灰色預測有關，以改進預測模型的準確性。本研究結果具有以下的貢獻：一、應用泰勒近似法於灰色預測及其在教育資訊與測驗統計所預測的問題，特別是使用泰勒近似法於RaschGSP IRT可以改進RaschGSP IRT的準確度和最優化係數α，β和γ。二、使用泰勒近似法於灰色預測結合灰關聯分析(Grey Relational Analysis, GRA)，來預測和評估學生的成就時，同時使用泰勒近似法於灰色預測結合灰關聯分析與接收者操作特徵(Receiver Operating Characteristic, ROC)，來建立測試標準設定。三、達成了研究和學習灰色系統理論的目的，基於泰勒近似法於灰色預測建立了一個MATLAB工具箱。實驗結果顯示，泰勒近似法於灰色預測、灰關聯分析與接收者操作特徵對系統不明確性及資訊不完整性之預測問題、評估、測試標準應用在教育資訊與測驗統計具有實際的效用價值。
The purpose of this study proposes to apply Taylor approximation method in grey prediction (TAMGP) to educational information and measurement. TAMGP is developed based on the combination of Taylor approximation method and grey prediction of grey system theory. In 1982, grey system theory was first proposed by Deng. In recent years, the grey system theory has also been successfully employed in various prediction applications. It has become a very effective method of solving uncertainty problems under discrete data and incomplete information. In educational information and measurement, when the number of data in the system is not enough for traditional statistical methods, the application of grey system theory can get good results in which grey prediction models play a very important role for prediction problems. However, there is a problem that the predicted accuracy of grey models is unsatisfied. The coefficients of the prediction models are not the optimal coefficients. Therefore, using TAMGP can obtain the most optimal prediction values by multi-times approximate calculation. The research approach adopted in this dissertation includes theoretical study and experimental study related to Taylor approximation method in grey prediction to improve the accuracy of the previous prediction models. The findings from this study are shown as follows: (1) Applying TAMGP in educational information and measurement for prediction problems, especially using Taylor approximation method in RaschGSP IRT to improve the accuracy and to optimize coefficients α, β and γ of RaschGSP IRT. (2) Using the combination of TAMGP and GRA to predict and evaluate the academic achievement of students, and using the combination of TAMGP, GRA, and ROC to build setting the standard for tests. (3) Developing a MATLAB toolbox based on TAMGP for the purpose of the study and learning of grey system theory. The experimental results showed that TAMGP, GRA, and ROC are actually useful for prediction problems, evaluation, and setting the standard for tests of uncertainty systems and incomplete information in educational information and measurement.
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