We consider the two Higgs doublet model (2HDM) of type III which leads to flavor changing neutral currents (FCNC) at the tree level. In the framework of this model we can have, in principle, two situations: the case (a) when both doublets acquire a vacuum expectation value different from zero and the case (b) when one of them is zero. In addition, we show that we can make two types of rotations for the flavor mixing matrices which generates four types of different Lagrangians. Two of the four possible Lagrangians correspond to the 2HDM type I and type II plus flavor changing (FC) interactions. The analytical expressions of the partial lepton number violating widths $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}eee)$ and $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma})$ are derived for the cases (a) and (b) and both types of rotations. In all cases these widths go asymptotically to zero in the limit when all Higgs boson masses go to infinity. We present from our analysis upper bounds for the flavor changing transition $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e,$ and we show that such bounds are sensitive to the VEV structure and the type of rotation utilized.