The well-known Sugeno’s Lambda-measure can only be used for real data fit to subadditive, additive, or super-additive fuzzy measures, which cannot be mixed with any fuzzy measure. To overcome this disadvantage, Grabisch extended the fuzzy density function from the first order to the second order, in order to propose his 2-additive fuzzy measure. We know that the 2-additive fuzzy measure is only a univalent fuzzy measure. Hsiang-Chuan Liu has proposed an improved multivalent fuzzy measure based on a 2-additive fuzzy measure, called Liu’s second order multivalent fuzzy measure. It is more sensitive and useful than a 2-additive fuzzy measure, since it is a generalization of the 2-additive fuzzy measure. However, the fuzzy density functions of all of the above mentioned fuzzy measures can only be used for unsupervised data. In this paper, we have proposed the corresponding ones for the supervised data. In order to compare the Choquet integral regression model with P-measure,?-measure, Liu’ multivalent fuzzy measure, 2-additive measure, and Liu’ second order multivalent fuzzy measure based on Liu’s supervised fuzzy density function, the traditional multiple regression model and the ridge regression model, a real data experiment by using a 5-fold cross validation Mean Square Error (MSE) is conducted. Results show that the Choquet integral regression model with Liu’ second order multivalent fuzzy measure has the best performance.