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

For the same fuzzy support, gamma-support, there is only one solution of measure function for both well-known fuzzy measures, lambda-measure and P-measure. In this study, we considered the power measures of lambda-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, lambda-measure, power measures of P-measure, and power measures of lambda-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 lambda-measure outperforms the other models.