Let's examine the transfer of the conflicting qualitative mass qm∧(A∩B) = qm∧(∅) = L13 6 to the non-empty sets according to the main following combination rules:
- **Qualitative Dempster's rule** (extension of classical numerical DS rule to qualitative masses): Assuming Shafer's model for the frame Θ (*i.e.* A ∩ B = ∅) and according to DS rule, the conflicting qualitative mass qm∧(A ∩ B) = L13 6is redistributed to the sets A, B, A ∪ B proportionally with their qm∧(.) masses L13 6
, L86
, and L2 6 respectively:

$${\frac{x_{A}}{L_{\frac{13}{6}}}}={\frac{y_{B}}{L_{\frac{2}{6}}}}={\frac{z_{A\cup B}}{L_{\frac{2}{6}}}}={\frac{L_{\frac{13}{6}}}{L_{\frac{13}{6}}+L_{\frac{2}{6}}+L_{\frac{2}{6}}}}={\frac{L_{\frac{13}{6}}}{L_{\frac{23}{6}}}}=L_{({\frac{13}{6}}+{\frac{23}{6}})\cdot6}=L_{({\frac{13}{22}})\cdot6}=L_{\frac{23}{22}}$$

Therefore, one gets:

$x_A=L_{\frac{13}{6}}\cdot L_{\frac{78}{23}}=L_{(\frac{13}{6}\cdot\frac{78}{23})\div6}=L_{\frac{169}{138}}$ 2. 
$$y_{B}=L_{\frac{8}{6}}\cdot L_{\frac{78}{23}}=L_{(\frac{8}{6}\cdot\frac{78}{23})\div6}=L_{\frac{104}{138}}$$
$$z_{A\cup B}=L_{\frac{2}{6}}\cdot L_{\frac{78}{23}}=L_{(\frac{2}{6},\frac{78}{23})\div6}=L_{\frac{26}{138}}$$
We can check that the qualitative conflicting mass, L13 6
, has been proportionally split into three qualitative masses:

$L_{\frac{169}{138}}+L_{\frac{104}{138}}+L_{\frac{26}{138}}=L_{\frac{169+104+26}{138}}=L_{\frac{299}{138}}=L_{\frac{13}{6}}$ ? 
So:

 $qm_{DS}(A)=L_{\frac{13}{6}}+L_{\frac{169}{138}}=L_{\frac{13}{6}+\frac{169}{138}}=L_{\frac{468}{138}}$  $qm_{DS}(B)=L_{\frac{8}{6}}+L_{\frac{104}{138}}=L_{\frac{8}{6}+\frac{104}{138}}=L_{\frac{288}{138}}$  $qm_{DS}(A\cup B)=L_{\frac{2}{6}}+L_{\frac{26}{138}}=L_{\frac{2}{6}+\frac{26}{138}}=L_{\frac{72}{138}}$  $qm_{DS}(A\cap B=\varnothing)=L_0$
qmDS(.) is quasi-normalized since:

$L_{\frac{468}{138}}+L_{\frac{288}{138}}+L_{\frac{72}{138}}=L_{\frac{828}{138}}=L_6=L_{\mathrm{max}}$. 

If we approximate the linguistic labels L468 138
, L288 138 and L 72 138 in order to work with original labels in L, still qmDS(.) remains quasi-normalized since:

$$q m_{D S}(A)\approx L_{[{\frac{468}{138}}]}=L_{3}$$
 $\\ qm_{DS}(B)\approx L_{[\frac{288}{138}]}=L_2\\ \\ qm_{DS}(A\cup B)\approx L_{[\frac{72}{138}]}=L_1$  . 
and $L_3+L_2+L_1=L_6=L_{\rm max}$. 