Inner estimates of the solution set of interval linear systems with precise coefficient matrices

Abstract

Finding "the best" interval solution for an interval system of linear equations is a problem known to be NP-hard. This paper provides a full characterization of inner interval estimates of the united solution set of formally consistent interval linear systems, where the coefficient matrix of arbitrary size is precise. This characterization is based on the generalized inverses of the real coefficient matrices. A straightforward approach for obtaining the united inner solution set of systems of linear interval equations with real coefficient matrices of arbitrary size is presented, accompanied by illustrative examples. Additionally, a necessary and sufficient condition for the equality of inner estimates and the maximal inner estimates of such systems is provided.