content_image/355747.jpg content_image/355746.jpg content_image/355744.jpg content_image/355743.jpg content_image/355742.jpg content_image/355741.jpg
We extend the FL symmetry as 

and the mass matrices Eqs. (6) and (7) as 

<img src='content_image/355747.jpg'>

<img src='content_image/355746.jpg'>

and 

<img src='content_image/355744.jpg'>

respectively. Here, we again assume that 

<img src='content_image/355743.jpg'>

Note that we extend the model so that the mass matrices keep the features mentioned just behind Eq. (8). Since a detailed analysis goes beyond the purpose of the paper, we would like to roughly study and try to figure out their implications. Both Eqs. (27) and (28) are diagonalized by real orthogonal matrices. One can easily find that ρ$_{q}$ determine the mass ratios of the fourth and third generation quarks: 

<img src='content_image/355742.jpg'>

where t ′ and b ′ indicate the fourth generation quarks, and all coefficients are omitted. The fourth generation quark mixings with the other three generations can also be estimated as 

<img src='content_image/355741.jpg'>

