  The interval numbers is the set of compact intervals of $\mathbb{R}$ with
addition and multiplication operation, which are very useful for solving
calculations where there are intervals of error or uncertainty, however, it
lacks an algebraic structure with an inverse element, both additive and
multiplicative This fundamental disadvantage results in overestimation of
solutions in an interval equation or also overestimation of the image of a
function over square regions. In this article we will present a solution to
this problem, through a morphism that preserves both the addiction and the
multiplication between the space of the interval numbers to the space of square
diagonal matrices.
