  The common behaviour of many families of numerical semigroups led up to
defining, firstly, the Frobenius varieties and, secondly, the (Frobenius)
pseudo-varieties. However, some interesting families are still out of these
definitions. To overcome this situation, here we introduce the concept of
restricted Frobenius variety (or R-variety). We will generalize most of the
results for varieties and pseudo-varieties to R-varieties. In particular, we
will study the tree structure that arise within them.
