An interval linear tolerance problem

This paper is concerned with a tolerance problem for an interval linear system $\boldsymbol Ax=\boldsymbol b$ requiring inner estimation of the admissible solution set $\{x\in\mathbb{R}^n \mid(\forall A\in\boldsymbol A)(Ax\in\boldsymbol b)\}$ formed by vectors $x$ for which the product $Ax$ remains within $\boldsymbol b$ for any possible $A\in\boldsymbol A$. Methods for verifying the emptiness and nonemptiness of admissible solution sets are developed. Formulas for the dimensions of the interval solution of a tolerance problem with known center are derived.

Presented by the member of Editorial Board: A. I. Kibzun