Choquet Integral with Respect to Extensional L-measure and its Application

Abstract

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