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題名：結合完全L-測度與Delta-測度之複合模糊測度之CHOQUET積分
作者：吳德邦
作者(外文)：Der-bang Wu
校院名稱：國立臺中教育大學
系所名稱：教育測驗統計研究所
指導教授：劉湘川博士
許天維博士
學位類別：博士
出版日期：2010
主題關鍵詞：λ-測度；P-測度；L-測度；δ-測度；L(δ)-模糊測度；γ-密度函數；Choquet模糊積分；完全模糊測度L(Cδ)；λ-measure；P-measure；L-measure；δ-measure；L(δ)-measure；γ-Density Function；Choquet integral；L(Cδ)-measure
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如眾所周知，傳統的λ-測度和P-測度，均僅具有唯一公式解。Liu, et. al. (2008, 2009)為了改善此一缺失與限制，先後分別提出具有無窮多解的L-測度與δ-測度，但L-測度並不是可加性測度，而且δ-測度之多值測度解之範圍比L-測度之多值測度解之範圍小很多。
由於上述兩種測度各有其優略，為了結合優點，避除缺點，結合L-測度與半個δ-測度，Liu發表複合模糊測度模式(Liu, et. al., 2009)。本研究更上一層樓，提出更為改善的模糊測度，結合L-測度與全部的δ-測度，稱之為「結合完全L-測度與Delta-測度之複合模糊測度模式」，記做L(Cδ)。
研究結果顯示：結合完全L-測度與Delta-測度之複合模糊測度模式，L(Cδ)，在基於 -密度函數之Choquet模糊積分迴歸模式之預測效力優於其他預測模式。
關鍵字：λ-測度，P-測度，L-測度，δ-測度，L(δ)-模糊測度， 密度函數，
Choquet模糊積分，完全模糊測度
In this dissertation, a composed fuzzy measure of completed L-measure and δ-measure, denoted -measure, is proposed. This new measure is proved that it is of closed form with infinitely many solutions, and can be considered as an extension of the three well known measures, additive measure, λ-measure and P-measure, respectively. Furthermore, it is a completed multivalent fuzzy measure, and not only including the smallest fuzzy measure, P-measure, but also attaining to the largest fuzzy measure, B-measure. It has more infinitely many fuzzy measure solutions than L-measure, δ-measure and the composed fuzzy measure of L-measure, and δ-measure. By using 5-fold cross-validation MSE, a real data experiment is conducted for comparing the performances of a multiple linear regression model, a ridge regression model, and the Choquet integral regression model with respect to P-measure, λ-measure, δ-measure, L-measure, L(δ)--measure, L(C)--measure and L(Cδ)-measure, respectively.
The result shows that the Choquet integral regression models with respect to the proposed L(Cδ)--measure outperforms other forecasting models.
KEY WORDS: λ-measure, P-measure, L-measure, δ-measure, L(δ)-measure, γ-Density Function, Choquet integral, L(Cδ)-measure
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