Discussion Of The Nonlinear Multiregressions Model Based On Choquet Integral

Establishment of regression model is an important part of regression analysis. The nonlinear multiregression models based on Choquet integrals have shown successful applications in practice since the adopted nonadditive set functions in Choquet integrals can effectively describe interaction among the attributes invovled. In the existing nonlinear multiregressin models, the nonlinear integrals are with respect to real-valued set functions. However, in some real problems, it seems more reasonable that the set functions are interval or fuzzy numbers. In this paper, a nonlinear multiregression model is designed based on Choquet integral with respect to an interval-valued signed fuzzy measure. The generalized Choquet integral in the model can be calculated by Linear Programming. Furthermore, we determine the regression coefficients optimally using a population evolutionary algorithm. Experimental results demonstrate the feasibility and effectiveness of the algorithm.