Proceedings of 2009 International Symposium on Computer Science and Computational Technology (ISCSCT 2009) Huangshan, China, December 2628, 2009 Editors: Fei Yu, Guangxue Yue, Jian Shu, Yun Liu AP Catalog Number: APPROCCS09CN005 ISBN: 9789525726077 (Print), 9789525726084 (CDROM) Page(s): 201204 

Type II Composed Fuzzy Measure of Lmeasur and Deltameasure HsiangChuan Liu, Derbang Wu, WeiSung Chen, HsienChang Tsai, YuDu Jheng, and TianWei Sheu 
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Abstract 

The well known fuzzy measures, λmeasure and Pmeasure, have only one formulaic solution. Two multivalent fuzzy measures with infinitely many solutions were proposed by our previous works, called Lmeasure and δmeasure, but the former does not include the additive measure as the latter and the latter has not so many measure solutions as the former. Due to the above drawbacks, an improved fuzzy measure composed of Lmeasure and half of δmeasure, denoted L(δ)measure, was proposed by our other previous work. In this paper, a further improved fuzzy measure composed of Lmeasure and the whole of δmeasure, called Type II L(δ)measure is proposed. For evaluating the Choquet integral regression models with the new fuzzy measure and other different ones, a real data experiment by using a 5fold crossvalidation mean square error (MSE) is conducted. The performances of Choquet integral regression models with fuzzy measure based on Type II L(δ)measure, L(δ)measure, Lmeasure, δmeasure, λmeasure, and Pmeasure, respectively, a ridge regression model, and a multiple linear regression model are compared. Experimental result shows that the Choquet integral regression models with respect to Type II L(δ)measure outperforms others forecasting models. 

Index Terms 

Lambdameasure, Pmeasure, Deltameasure, composed fuzzy measure, Choquet integral 

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