Maximized L-Measure and Its Choquet Integral Regression Model

Abstract

The well known normalized monotone measures, λ-measure and P-measure, have only one formulaic solution. A multivalent normalized monotone measure with infinitely many solutions was proposed by our previous work, called L-measure, but L-measure is not a completed measure. And then, a completed measure with more many solutions than L-measure, called completed L-measure, was proposed by our next previous work, In this paper, a further improved completed measure, called maximized L-measure, is proposed. This new measure is more sensitive than completed L-measure. For evaluating the Choquet integral regression models with our proposed new measures 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 normalized monotone measure based on maximized L-measure, completed L-measure, 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 maximized L-measure based on γ-support outperforms other forecasting models.