Residual implications on the set of discrete fuzzy numbers

In this paper residual implications defined on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers are studied. A specific construction of these implications is given and some examples are presented showing in particular that such a construction generalizes the case of interval-valued residual implications. The most usual properties for these operations are investigated leading to a residuated lattice structure on the set of discrete fuzzy numbers, that in general is not an MTL-algebra.