¹Department of Bioinformatics and Medical Informatics, Asia University, Taichung, Taiwan; Graduate Institute of Acupuncture Science, China Medical University, Taichung, Taiwan
²Graduate School of Educational Measurement and Statistics, National Taichung University of Education, Taichung, Taiwan
³Department of Biology, National Changhua University of Education, Changhua, Taiwan
⁴Graduate School of Criminology, National Taipei University, Taipei, Taiwan; Department of criminal justice, Military Police School, Taipei, Taiwan

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Abstract—In this paper, a new fuzzy density function, called N-density, is proposed. A real data set about Students Valuing Science with 5-fold cross-validation RMSE is conducted, for comparing the performances of the Choquet integral regression model with respect to six measures, Pmeasure, λ-measure, L-measure, extensional L-measure, completed L-measure and extensional completed L-measure based on this new density and the old fuzzy support fuzzy density function, R-density, respectively, and two traditional regression model, multiple regression model and ridge regression model, the results show that the Choquet integral regression model with respect to each given fuzzy measure based on the new fuzzy density function is better than which based on the old fuzzy density function, and among all of the regression models, Choquet integral with respect to extensional completed L-measure based on N-density has the best performance.

Index Terms—Choquet integral, R-density, N-density, lambda measure, extensional completed L-measure.

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Cite: Hsiang-Chuan Liu, Yen-Kuei Yu, Hsien-Chang Tsai, Tung-Sheng Liu, "Choquet Integral with Respect to Extensional Completed L-Measure Based on N-Density," Journal of Computers vol. 7, no. 5, pp. 1122-1129, 2012.