A solution x to a system of interval linear equations Ax=b possesses its own semantics, which may involve combinations of tolerance, control, left- and right-localized semantics. In scenarios where the need arises to persist with a solution x despite changes in its semantics, corresponding adjustments in the interval information of the system become necessary. Our focus is on perturbing the original interval matrix A to produce a transformed matrix A′, ensuring that the solution x to A′x=b aligns with the new semantics. We present a series of theorems using quadratic programming concepts to determine A′ in a manner that closely approximates A. Several applications are provided to illustrate the practical utility of our approach.