  Fring and al in their paper entitled "Strings from position-dependent
noncommutativity" have introduced a new set of noncommutative space commutation
relations in two space dimensions. It had been shown that any fundamental
objects introduced in this space-space non-commutativity are string-like.
Taking this result into account, we generalize the seminal work of Fring and al
to the case that there is also a maximal length from position-dependent
noncommutativity and minimal momentum arising from generalized versions of
Heisenberg's uncertainty relations. The existence of maximal length is related
to the presence of an extra, first order term in particle's length that
provides the basic difference of our analysis with theirs. This maximal length
breaks up the well known singularity problem of space time. We establish
different representations of this noncommutative space and finally we study
some basic and interesting quantum mechanical systems in these new variables.
