The Choquet Integral with Respect to R-Measure Based on Gamma-Support

Abstract

When the multicollinearity within independent variables occurs in the multiple regression models, its performance will always be poor. Replacing the above models with the ridge regression model is the traditional improved method. In our previous work, we found that, the Choquet integral regression model with lambda-measure based on the new support, gamma-support, proposed by us has the best performance than before. In this study, for finding the further improved model, we replaced two well known fuzzy measures, P-measure and lambda-measure with our new fuzzy measure, R-measure in Choquet integral regression model with the new support, gamma-support. For comparing the Choquet integral regression model with P-measure, lambda-measure and R-measure based on two different fuzzy supports, V-support and gamma-support, respectively, 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. Experimental result shows that the Choquet integral regression model with R-measure based on gamma-support has the best performance.