
$$L_{i}(\epsilon_{i})+L_{j}(\epsilon_{j})=\begin{cases}L_{n+1}(c)&\text{if}\quad i+j\geq n+1,\\ L_{i+j}(c)&\text{otherwise.}\end{cases}\tag{1}$$

- qe**-multiplication of linguistic labels**
a) As direct extension of (6), the multiplication of enriched labels is defined by Li(ǫi) × Lj (ǫj ) = L[(i·j)/(n+1)](c**) (14)**
b) as another multiplication of labels, easier, but less exact:

$$L_{i}(\epsilon_{i})\times L_{j}(\epsilon_{j})=L_{\operatorname*{min}\{i,j\}}(c)$$
Li(ǫi) × Lj(ǫj ) = Lmin{i,j}(c**) (15)**
- **Scalar multiplication of a enriched label**
Let a **be a real number. We define the multiplication of an enriched linguistic label by a scalar as follows:**

$$a\cdot L_{i}(\epsilon_{i})\approx\begin{cases}L_{[a\cdot i]}(\epsilon_{i})&\text{if}[a\cdot i]\geq0,\\ L_{-[a\cdot i]}(\epsilon_{i})&\text{otherwise.}\end{cases}\tag{1}$$

- qe**-division of enriched labels**

 $\textbf{Division as an}$. 
$$\mathbf{a})$$
a) Division as an internal operator:
$$(17)$$
$${\frac{L_{i}(\epsilon_{i})}{L_{j}(\epsilon_{j})}}={\begin{cases}L_{n+1}(c)&{\mathrm{if~}}[(i/j)\cdot(n+1)]\geq n+1,\\ L_{[(i/j)\cdot(n+1)]}(c)&{\mathrm{otherwise.}}\end{cases}}$$
Let $j\neq0$, then . 
b) Division as an external operator:
Let j 6**= 0, then we can also consider the division of enriched labels as external operator too as follows:**

$$(19)$$

Li(ǫi) ⊘ Lj(ǫj ) = (i/j)supp(c) **(18)**

$(i/j)_{\text{sup}}$
The notation (i/j)supp(c) means that the numerical value (i/j**) is supported with the degree** c.

- qe**-subtraction of enriched labels**

$$L_{i}(\epsilon_{i})-L_{j}(\epsilon_{j})=\begin{cases}L_{i-j}(c)&\text{if}\quad i\geq j,\\ -L_{j-i}(c)&\text{if}\quad i<j.\end{cases}\tag{1}$$

These qe**-operators with numerical confidence degrees are consistent with the classical qualitative operators**
when ei = ej = 1 since c = 1 and Li(1) = Li for all i, and the qe**-operators with qualitative confidence degrees** are also consistent with the classical qualitative operators when ei = ej = O **(this is letter "O", not zero, hence**
the neutral qualitative confidence degree) since c = O **(neutral).**

## 6 Examples Of Qpcr5 Fusion Of Qualitative Belief Assignments 6.1 Qualitative Masses Using Quantitative Enriched Labels

Let's consider a simple frame Θ = {A, B} with Shafer's model (i.e. A∩B = ∅**), two qualitative belief assignments**
qm1(·) and qm2(·), the set of ordered linguistic labels L = {L0, L1, L2, L3, L4, L5, L6}, n **= 5, enriched with**
quantitative support degree (i.e. enriched labels of Type 1). For this example the (prudent) min operator for combining confidences proposed in section 5 (case b) ) is used, but other methods a) and c) can also be applied.We consider the following qbba summarized in the Table 1:

$$\left(13\right)$$
$$\left(14\right)$$
$$(15)$$
$$(16)$$

8