  Based on the analytic property of the symmetric $q$-exponent $e_q(x)$, a new
symmetric $q$-deformed Kadomtsev-Petviashvili ($q$-KP) hierarchy associated
with the symmetric $q$-derivative operator $\partial_q$ is constructed.
Furthermore, the symmetric $q$-CKP hierarchy and symmetric $q$-BKP hierarchy
are defined. Here we also investigate the additional symmetries of the
symmetric $q$-KP hierarchy.
