During the 50's, Moore and Sunaga proposed an arithmetic for closed intervals, $[a,b]=\{x\in R: a\leq x\leq b\}$, in order to provide an object able to capture the numerical errors during computations. The idea is that if we want to compute a value, $f(x)$, for  a function $f:\mathbb{R}\to \mathbb{R}$, the user provide an interval $[a,b]$ such that $x\in [a,b]$ and the composition of interval arithmetical operations, a function $F: I\mathbb{R}\to I\mathbb{R}$, provides the value $F([a,b])=[c,d]$, such that $f(x)\in F([a,b])$. This property is known as interval correctness. In 2006, Santiago and Bedregal investigated it from a topological viewpoint. The result was a method called interval representation, which is a way to define interval functions from real functions. This method has been efficient in applications and in the definition of Fuzzy connectives. The concept of interval and its arithmetic is the basis for the most important definition in Fuzzy theory, however some problems arise because the algebraic structure of intervals. In this talk we discuss some connections between Interval Mathematics and Fuzzy Logic.