A new nonlinear multiregression model based on a pair of extreme nonlinear integrals, upper and lower nonlinear integrals with respect to signed fuzzy measure, is established in this paper. A data set with the predictive features and the relevant objective feature is required for estimating the regression coefficients. Owing to the nonadditivity of the model, a multiobjective optimization using genetic algorithm is adopted to search for the optimized solution in the regression problem. Applying such a nonlinear multiregression model, an interval prediction for the value of the objective feature can be made once a new observation of predictive features is available. We apply our model on synthetic data and weather problem. The results testify the performance of the multiregression based on upper and lower nonlinear integrals.