The Choquet integral with respect to λ-measure based on γ-support

Abstract

When the multicollinearity between independent variables occurs in the multiple regression models, its performance will always be poor. The traditional improved method which is always used is the ridge regression model. Recently, the Choquet integral regression model with fuzzy measure can further be exploited to improve this situation. In this study, we found that based on different fuzzy support, the Choquet integral regression model with the same fuzzy measure may have different performances, three kinds of fuzzy supports, C-support, V-support and γ-support proposed by our work were considered. For evaluating the performances of the Choquet integral regression models with P-measure or λ-measure based on above different fuzzy supports, 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 λ-measure based on γ-support has the best performance.