  We generalize the ordinary Wess-Zumino model to the Bosonic-Fermionic
noncommutative (BFNC) superspace and study its renormalization. In our previous
work that can be regarded as the key foundation of the present paper, we have
proved that the BFNC Wess-Zumino model with the real mass and interacting
constant is one-loop renormalizable up to the second order of BFNC parameters.
Based on the result obtained, in the present paper we modify the one-loop
renormalizable BFNC Wess-Zumino model by generalizing the mass and interacting
constant to complex numbers, introduce the U(1)_{R} R-symmetry and U(1)_{\Phi}
flavor symmetry in the modified model, analyze possible divergent operators in
the effective action of the modified model by using the dimensional analysis
method, and further give a new BFNC Wess-Zumino model that is renormalizable at
all loops still up to the second order of BFNC parameters by imposing
symmetries rather than doing a direct perturbative investigation.
