Choquet integral regression model based on high-order L-measure

Abstract

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution, the former is not a closed form, and the later is not sensitive. An improved multivalent fuzzy measure with infinitely many solutions of closed form, called L-measure, is proposed by our previous work. In this paper, expend the L-measure for being more choice, and get an improved fuzzy measures, called “hth-order L-measure”, denoted as Lh-measure, and a new Choquet integral regression model based on this Lh-measure is also proposed. For evaluating the proposed regression models with different fuzzy measures, 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 λ-measure, P-measure, L-measure and Lh-measure, respectively, a ridge regression model, and a multiple linear regression model are compared. Experimental result shows that the Choquet integral regression models with Lh-measure based on γ-support outperforms others forecasting models.