Theory and application of the composed fuzzy measure of L-measure and delta-measures

Abstract

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. Two multivalent fuzzy measures with infinitely many solutions were proposed by our previous works, called L-measure and δ-measure, but the former do not include the additive measure as the latter and the latter has not so many measure solutions as the former. Due to the above drawbacks, in this paper, an improved fuzzy measure composed of above both, denoted Lδ -measure, is proposed. 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 Lδ -measure, L-measure, δ-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 L-measure based on γ-support outperforms others forecasting models.