CHOQUET INTEGRAL WITH RESPECT TO THE COMPOSED FUZZY MEASURE OF COMPLETED L-MEASURE AND DELTA-MEASURE

• Main Authors: Der-bang Wu, 吳德邦
• Other Authors: Hsiang-Chuan Liu
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/81405587972104607815

博士 === 國立臺中教育大學 === 教育測驗統計研究所 === 98 === 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