Choquet integral with respect to extensional L-measure and its application

  • Authors:

  • Hsiang-Chuan Liu;Chin-Chun Chen;Yu-Du Jheng;Maw-Fa Chien

  • Affiliations:

  • Department of Bioinformatics, Asia University, Taiwan;Graduate Institute of Educational Measurement and Statistics, Taichung University, Taichung, Taiwan and Department of General Education Min-Hwei College, Taiwan;Graduate Institute of Educational Measurement and Statistics, Taichung University, Taichung, Taiwan;College Entrance Examination Center, Taiwan

  • Venue:
  • FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 6
  • Year:
  • 2009

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Abstract

The well known fuzzy measures, λ-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 λ-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, 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 extensional L-measure based on γ-support outperforms others forecasting models.