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Proceedings of 2009 International Symposium on Computer Science and Computational Technology (ISCSCT 2009)

Huangshan, China, December 26-28, 2009

Editors: Fei Yu, Guangxue Yue, Jian Shu, Yun Liu

AP Catalog Number: AP-PROC-CS-09CN005

ISBN: 978-952-5726-07-7 (Print), 978-952-5726-08-4 (CD-ROM)

Page(s): 201-204

Type II Composed Fuzzy Measure of L-measur and Delta-measure

HsiangChuan Liu, Derbang Wu, WeiSung Chen, HsienChang Tsai, YuDu Jheng, and TianWei Sheu

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The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. Two multivalent fuzzy measures with infinitely many solutions were proposed by our previous works, called L-measure and δ-measure, 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 L-measure and half of δ-measure, denoted L(δ)-measure, was proposed by our other previous work. In this paper, a further improved fuzzy measure composed of L-measure and the whole of δ-measure, 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 5-fold cross-validation 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, L-measure, δ-measure, λ-measure, and P-measure, 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

Lambda-measure, P-measure, Delta-measure, composed fuzzy measure, Choquet integral

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