| Summary: | 碩士 === 國立臺中教育大學 === 教育測驗統計研究所 === 98 === When multicollinearity among independent variables exist in forecasting problems, the performance of the multiple linear regression model is not good enough. The traditional improved methods exploited the ridge regression models. In recent years, a improved method, Choquet integral regression model with monotone measure, was proposed.
L-measure is a multivalent monotone measure, which has better performance than other measures with infinite solutions, but it dose not include additive measure. In this study, a improved monotone measure, extensional L-measure, is developed. P-measure, additive measure, and λ-measure are kinds of special case of extensional L-measure.
For evaluating the Choquet integral regression models with our developed fuzzy measure and other different ones, an educational data experiment by using 5-fold cross-validation mean square error (MSE) is conducted.
The performances of Choquet integral regression models with monotone measure based on respective extensional L-measure , L-measure, λ-measure, and P-measure, a ridge regression model, and a multiple linear regression model are compared.Experimental result shows that the Choquet integral regression models with extensional L-measure outperforms others forecasting models.
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