A new model of nonlinear multiregressions by projection pursuit based on generalized Choquet integrals

A nonlinear multiregression model is presented based on the generalized Choquet integral with respect to a signed fuzzy measure. In this model, the interaction among predictive attributes toward the objective attribute is depicted by a signed fuzzy measure. To guarantee the invariability of the multiregression under scale variation and translation of the attributes, a respective linear transformation with unknown coefficients is applied to each attribute. All of these coefficients and the values of the signed fuzzy measure are optimally determined as the regression coefficients by running an adaptive genetic algorithm based on given data.