Extensionally Completed L-measure Based on any Given Fuzzy Measure

Abstract

The well known fuzzy measures, λ-measure and P-measure, both of them have only one formulaic solution. A multivalent fuzzy measure with infinitely many solutions was proposed by our previous work, called L-measure, but it is not a completed measure. After that, an improved completed measure with more many solutions than L-measure, called complete L-measure, was also proposed by the author. In this paper, the extensionally completed L-measure is proposed. Some properties of this new measure are discussed, it is proved that not only λ-measure and P-measure but also any given fuzzy measures are the special cases of this new 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 fuzzy measure based on 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 model with respect to the new measure outperforms other forecasting models.