Choquet integral with respect to sigma-fuzzy measure

Both the well known fuzzy measures, ¿-measure and P-measure, have only one formulaic solution, the former is not a closed form, and the latter not sensitive enough. In this paper, A novel multivalent fuzzy measure with infinitely many solutions, called ¿-measure, is proposed. This new measure can be considered as an extension of the P-measure and ¿-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 ¿-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 ¿-measure based on ¿-support outperforms other forecasting models.