Power-transformed-measure and its Choquet integral regression model

Both the well known fuzzy measures, lambda-measure and P-measure, have only one solution of measure function with no more choice. In this study, we propose the power-transformed-measures for any given fuzzy measure, those new measures with infinitely many solution of measure function can be chosen the best one to apply for improving the forecasting performances. A real data experiment by using a 5-fold cross-validation mean square error (MSE) is conducted. The performances of four Choquet integral regression models based on lambda-measure, P-measure, power-transformed-measures of lambda-measure, and power-transformed-measures of P-measure, respectively, 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 the proposed power-transformed-measures outperform the performances of other models.