\\
&+& L_{L3}N_{R3}\left[Y_{2}H_{3} + Y_{3}\Phi_{3}\right] + L_{L3}(N^{(2)}_{R} + N^{(3)}_{R})\left[Y_{2}H_{3} + Y_{3}\Phi_{3}\right] \;\;.\end{aligned}$$ We see that the linear combination of the two $A_{4}$ triplet fields, $H_{3}$ and $\Phi_{3}$, contribute to the Dirac neutrino masses. One can decouple the fourth generation neutrino from the three light generations and satisfy the conditions of tribimaximal mixings by assuming the VEVs of $H_{3}$ are relatively small compare to the VEVs of $\Phi_{3}$ as we will demonstrate below. Hence the Dirac matrix of the neutrino sector $M_{D}$ is given by $$\begin{aligned}
&&\nu_{L}M_{D}N^T_{R} = \nonumber \\
&&\left(\begin{array}{cccc}\nu_{L1} & \nu_{L3_1} & \nu_{L3_2} & \nu_{L3_3}\end{array}\right)
\left(\begin{array}{cccccc}Y_{1}v_{H_1} & 0 & 0 & Y_{3}v_{\phi_1} & Y_{3}v_{\phi_2} & Y_{3}v_{\phi_3} \\ 0 & Y_{3}v_{\phi_1} & Y_{3}v_{\phi_1} & Y_{2}v_{H_1} & Y_{3}v_{\phi_3} & Y_{3}v_{\phi_2} \\ 0 & \omega Y_{3}v_{\phi_2} & \omega^2Y_{3}v_{\phi_2} & Y_{3}v_{\phi_3} & Y_{2}v_{H_1} & Y_{3}v_{\phi_1} \\ 0 & \omega^2Y_{3}v_{\phi_3} & \omega Y_{3}v_{\phi_3} & Y_{3}v_{\phi_2} & Y_{3}v_{\phi_1} & Y_{2}v_{H_1}\end{array}\right)\left(\begin{array}{c}N^{(1)}_{R} \\N^{(2)}_{R} \\N^{(3)}_{R} \\N_{R3_{1}} \\N_{R3_{2}} \\ N_{R3_{3}}\end{array}\right) 
\nonumber  \;\;,\\\end{aligned}$$ where we set the VEVs $\langle \Phi_{3}\rangle = (v_{\phi_1}, v_{\phi_2}, v_{\phi_3})$ and $\langle H_{1}\rangle = v_{H_1}$.

The left-handed Majorana mass matrix $M_{\nu_{L}}$ is obtained by the seesaw mechanism, $$\begin{aligned}
M_{\nu_{L}} = M_{D}M^{-1}_{N_{R}}M^{T}_{D} \;\;, \end{aligned}$$ thus the ten components of the $4\times4$ symmetric matrix can be written as 