Choquet integral with respect to sigma-fuzzy measure

Abstract

Both the well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution, the former is not a closed form, and the latter not sensitive enough. In this paper, A novel multivalent fuzzy measure with infinitely many solutions, called σ-measure, is proposed. This new measure can be considered as an extension of the P- measure andλ- measure, For evaluating the Choquet integral regression models with our proposed fuzzy measure and other different ones, a real data experiment by using a 5-fold cross-validation mean square error (MSE) is conducted. The performances of Choquet integral regression models with fuzzy measure based on σ-measure, λ-measure and P-measure, respectively, a ridge regression model and a multiple linear regression model are compared. Experimental result shows that the Choquet integral regression models with respect to σ-measure based on γ-support outperforms other forecasting models.