Choquet integral with respect to power measure of lamda measure with gamma support

For the same fuzzy support, γ-support, there is only one solution of measure function for both well-known fuzzy measures, λ-measure and P-measure. In this study, we considered the power measures of λ-measure and P-measure respectively, those new measures with infinitely many solutions of measure function can be chosen the best one to improve the forecasting performances for the given fuzzy measure. A real data by using a leave one out cross-validation and mean square error are conducted in this research. The performances of four Choquet integral regression models based on P-measure, λ-measure, power measures of P-measure, and power measures of λ-measure, respectively, a ridge regression model, and the traditional multiple linear regression model are compared. Experimental results show that the performances of Choquet integral regression model based on our proposed power measure of λ-measure outperforms the other models.