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Type II Composed Fuzzy Measure of L-measure and Delta-measure

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 does 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, an improved fuzzy measure composed of Lmeasure and half of δ-measure, denoted L(δ)-measure, was proposed by our other previous work. In this paper, a further improved fuzzy measure composed of L-measure and the whole of δ-measure, called Type II L(δ)-measure is proposed. For evaluating the Choquet integral regression models with the new 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 Type II L(δ)-measure, L(δ)-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 Type II L(δ)measure outperforms others forecasting models.