Title :
Choquet Integral with Respect to Extensional L-measure and its Application
Author :
Liu, Hsiang-chuan ; Chen, Chin-chun ; Jheng, Yu-Du ; Chien, Maw-Fa
Author_Institution :
Dept. of Bioinf., Asia Univ., Taiwan
Abstract :
The well known fuzzy measures, ¿-measure and P-measure, have only one formulaic solution. An multivalent fuzzy measure with infinitely many solutions of closed form based on P-measure was proposed by our previous work, called L-measure, In this paper, A further improved fuzzy measure, called extensional L-measure, is proposed. This new fuzzy measure is proved that it is not only an extension of L-measure but also can be considered as an extension of the ¿-measure and P-measure. For evaluating the Choquet integral regression models with our proposed 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 extensional L-measure, L-measure, ¿-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 extensional L-measure based on ¿-support outperforms others forecasting models.
Keywords :
fuzzy set theory; regression analysis; 5-fold cross-validation mean square error; Choquet integral regression models; P-measure; extensional L-measure; multivalent fuzzy measure; ridge regression model; ¿-measure; Asia; Bioinformatics; Educational institutions; Fuzzy systems; Linear regression; Mean square error methods; Performance evaluation; Predictive models; Statistics; Choquet integral; L-measure; extensional L-measure; fuzzy measure;
Conference_Titel :
Fuzzy Systems and Knowledge Discovery, 2009. FSKD '09. Sixth International Conference on
Conference_Location :
Tianjin
Print_ISBN :
978-0-7695-3735-1
DOI :
10.1109/FSKD.2009.355