A Novel Approach for Nonlinear Interval Regression

Interval data exist widely in industry and real life because the influence of uncertain, imprecise and incomplete factors. In order to find the crisp relationship among these data, nonlinear interval regression is used as an important avenue. In former crisp input and interval output regression analysis, crude symmetrical estimation is obtained for interval data. For the asymmetrical interval data set which error ranges differ in the upper and lower ends, current approaches can´t be depict exactly. In this paper, asymmetrical interval data analysis is proposed for the first time. The two interval ends are studied independently, and three regression models are proposed to describe asymmetrical interval data. Support vector machine (SVM) is imported into this approach for its model-free character in nonlinear regression. A new nonlinear interval regression SVM (NIR-SVM) approach is proposed for the estimation of asymmetrical interval data. Experiments are presented to show the good performance of NIR-SVM. Based on the newly defined MAPE measure, the results of different approaches are compared and analyzed.