A non-linear multi-regression model based on the Choquet integral with a quadratic core. (1st January 2012) - Yan, Nian; Chen, Zhengxin; Shi, Yong; Wang, Zhenyuan
Signed efficiency measures with relevant non-linear integrals can be used to treat data that have strong interaction among contributions from various attributes towards a certain objective attribute. The Choquet integral is the most common non-linear integral. The non-linear multi-regression based on the Choquet integral can well describe the non-linear relation how the objective attribute depends on the predictive attributes. This research is to extend the non-linear multi-regression model from using a linear core to adopting a quadratic core in the Choquet integral. It can describe some more complex interaction among attributes and, therefore, can significantly improve the accuracy of non-linear multi-regression. The unknown parameters of the model involve the coefficients in the quadratic core and the values of the signed efficiency measure. They should be optimally determined via a genetic algorithm based on the given data. The results of the new model are compared with that of the linear core as well as the classic linear multi-regression that can be solved by an algebraic method.