Tolerance Approach to Possibilistic Nonlinear Regression With Interval Data

We study possibilistic nonlinear regression models with crisp and/or interval data. Herein, the task is to compute tight interval regression parameters such that all observed output data (either crisp or interval) are covered by the range of the nonlinear interval regression function. We propose a method for determination of interval regression parameters based on the tolerance approach developed by the authors for the linear case. We define two classes of nonlinear regression models for which efficient algorithms exist. For other models, we provide some extensions allowing to calculate lower and upper bounds on the widths of the optimal interval regression parameters. We also discuss other approaches to interval regression than the possibilistic one. We illustrate the theory by examples.