A Novel Fuzzy Measure and its Choquet Integral Regression Model

Abstract

The well known fuzzy measures, λ -measure and P-measure, have only one formulaic solution, the former is not a closed form, and the later is not sensitive. In this study, Sugeno, and Choquet integral regression models with a novel fuzzy measure, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> -measure, are proposed. The proposed L-measure has infinitely many closed-form solutions. For evaluating the proposed regression models with different fuzzy measures, a real data experiment by using a 5-fold cross-validation mean square error (MSE) is conducted. The performances of Sugeno, and Choquet integral regression models with fuzzy measure based on λ -measure, P-measure, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> -measure respectively, a ridge regression model, and a multiple linear regression model are compared. Experimental result shows that the Choquet integral regression models with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> -measure outperforms others forecasting models.