Choquet Integral with Respect to Extensional Completed L-Measure Based on N-Density

In this paper, a new fuzzy density function, called N-density,  is  proposed.  A  real  data  set  about  Students Valuing   Science   with   5-fold   cross-validation   RMSE   is conducted, for comparing the performances of the Choquet integral  regression  model  with  respect  to  six  measures,  P-measure,   λ-measure,   L-measure,   extensional   L-measure, completed L-measure and extensional completed L-measure based  on  this  new  density  and  the  old  fuzzy  support  fuzzy density function, R-density, respectively, and two traditional regression   model,   multiple   regression   model   and   ridge regression model, the results show that the Choquet integral regression  model  with  respect  to  each  given  fuzzy  measure based on the new fuzzy density function is better than which based on the old fuzzy density function, and among all of the regression   models,   Choquet   integral   with   respect   to extensional  completed  L-measure  based  on  N-density  has the best performance.