  It will be shown that the defining relations for fuzzy torus and deformed
(squashed) sphere proposed by J. Arnlind, et al (hep-th/0602290) (ABHHS) can be
rewriten as a new algebra which contains q-deformed commutators. The quantum
parameter q (|q|=1) is a function of \hbar. It is shown that the q -> 1 limit
of the algebra with the parameter \mu <0 describes fuzzy S^2 and that the
squashed S^2 with q \neq 1 and \mu <0 can be regarded as a new kind of quantum
S^2. Throughout the paper the value of the invariant of the algebra, which
defines the constraint for the surfaces, is not restricted to be 1. This allows
the parameter q to be treated as independent of N (the dimension of the
representation) and \mu. It was shown by ABHHS that there are two types of
representations for the algebra, ``string solution'' and ``loop solution''. The
``loop solution'' exists only for q a root of unity (q^N=1) and contains
undetermined parameters. The 'string solution' exists for generic values of q
(q^N \neq 1). In this paper we will explicitly construct the representation of
the q-deformed algebra for generic values of q (q^N \neq 1) and it is shown
that the allowed range of the value of q+q^{-1} must be restricted for each
fixed N.
