Extensional Completed L-measure and Its Choquet Integral Regression Model

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. A multivalent fuzzy measure with infinitely many solutions based on Pmeasure was proposed by our previous work, called completed L-measure. In this paper, a further improved fuzzy measure, called extensional completed L-measure, is proposed. This new fuzzy measure is proved that it is not only an extension of completed L-measure but also can be considered as an extension of the λ-measure and P-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 extensional completed L-measure, completed Lmeasure, L-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 extensional completed L-measure based on γ-support outperforms others forecasting models.