  In this article we develop the concepts of $\sigma$-relation and
$\sigma$-function, following the same steps as in Set Theory. First we define
the concept of ordered pair and then we build the Cartesian Product of
$\sigma$-sets so that we can define the concepts of $\sigma$-relation and
$\sigma$-function.
  Now, as in $\sigma$-Set Theory there exist the concepts of
$\sigma$-antielement and $\sigma$-antiset, we can build the new concepts of
$\sigma$-antifunction, antidentity and antinverse. Finally, in the case that a
$\sigma$-function $f:A\to B$ is bijective and there exist $A^{\st}$ and
$B^{\st}$ $\sigma$-antiset of $A$ and $B$, we get 16 different
$\sigma$-functions which are related in a diagram of $\sigma$-functions.
