approximation (i.e. using only labels in L2**) one gets**11
- **with qPCR5**
qP(θ6 ∪ θ7 ∪ θ8) ∈ [L1, L3]

$$\begin{array}{c}{{q P(\overline{{{\theta_{6}\cup\theta_{7}\cup\theta_{8}}}})\in[L_{0},L_{2}]}}\\ {{q P(\theta_{7}\cup\theta_{8})\in[L_{1},L_{3}]}}\\ {{q P(\overline{{{\theta_{7}\cup\theta_{8}}}})\in[L_{0},L_{2}]}}\\ {{q P(\theta_{8})\in[L_{1},L_{2}]}}\\ {{q P(\bar{\theta}_{8})\in[L_{1},L_{2}]}}\end{array}$$

- **with qPCR6**
qP(θ6 ∪ θ7 ∪ θ8) ∈ [L1, L2]

| qP(θ6 ∪ θ7 ∪ θ8) ∈ [L1, L2] qP(θ7 ∪ θ8) ∈ [L1, L2] qP(θ7 ∪ θ8) ∈ [L1, L2] qP(θ8) ∈ [L1, L2] qP( ¯θ8) ∈ [L1, L2]   |
|-------------------------------------------------------------------------------------------------------------------|

These results show that is is almost impossible to answer clearly and fairly to the question Q1 using the max of Bel or the max of Pl criteria based on such very inaccurate qualitative bba's using such crude approximation. However it is possible and easy to answer to Q1 using qualitative DSmP value. However and according to Table 66, the final decision must be to evacuate the building B when considering the level of DSmP values of θ6∪θ7∪θ8, θ7∪θ8**, or** θ8.

Answer to Q1 using refined approximation: **Using the refined approximation using refined labels which**
is more accurate, one gets

## - **With Qpcr5**

qP(θ6 ∪ θ7 ∪ θ8) ∈ [L1.07, L3]

| qP(θ6 ∪ θ7 ∪ θ8) ∈ [L0, L1.93] qP(θ7 ∪ θ8) ∈ [L0.79, L3] qP(θ7 ∪ θ8) ∈ [L0, L2.21] qP(θ8) ∈ [L0.79, L2.43] qP( ¯θ8) ∈ [L0.57, L2.21]   |
|----------------------------------------------------------------------------------------------------------------------------------------|

- **with qPCR6**
qP(θ6 ∪ θ7 ∪ θ8) ∈ [L1.18, L3]

qP(θ6 ∪ θ7 ∪ θ8) ∈ [L0, L1.82]
$$\begin{array}{c}{{q P(\theta_{7}\cup\theta_{8})\in[L_{0.79},L_{3}]}}\\ {{q P(\overline{{{\theta_{7}}\cup\theta_{8}}})\in[L_{0},L_{2.21}]}}\\ {{q P(\theta_{8})\in[L_{0.79},L_{2.52}]}}\\ {{q P(\bar{\theta}_{8})\in[L_{0.48},L_{2.21}]}}\end{array}$$
One sees that accuracy of the result obtained using refined labels allows us to take the decision more easily.

Indeed, using the refined approximation, it is possible here to take the decision based on the max of Bel, or on the max of Pl and whatever the decision-support hypothesis used (θ6 ∪θ7 ∪θ8, or θ7 ∪θ8, or θ8**), the answer**
to question Q1 is: **Evacuation of the building** B.

The same decision can also be taken from the analysis of qDSmP values as well when considering refined labels in Table 66.

4.2 Fusion of sources using L3 Here we propose to go further in our analysis and to use a bit more refined set of labels defined by L3.

We need to adapt the qualitative inputs of the VBIED
problem in order to work with L3. Example 11**: We propose to solve the VBIED problem** for the following qualitative inputs which reflects what is reported by the sources when using labels belonging to L3.

Table 67: Qualitative inputs based on L3.

| focal element   | qm0(.)   | qm1(.)   | qm2(.)   | qm3(.)   |
|-----------------|----------|----------|----------|----------|
| θ4 ∪ θ8         | L4       | L0       | L1       | L0       |
| θ6 ∪ θ8         | L0       | L3       | L0       | L1       |
| θ4 ∪ θ8         | L0       | L0       | L3       | L0       |
| It              | L0       | L1       | L0       | L3       |

Based on the equidistant labels assumption, one gets the following mapping between labels and numbers L0 ≡ 0, L1 ≡ 1/4, L2 ≡ 2/4, L3 ≡ 3/4 and L4 = 1 and therefore, the Table 67 is equivalent to the quantitative inputs table 68 (which are more close to the numerical values taken in Example 1 than the inputs chosen in Table 63 for Example 10).

| focal element   | m0(.)   | m1(.)   | m2(.)   | m3(.)   |
|-----------------|---------|---------|---------|---------|
| θ4 ∪ θ8         | 1       | 0       | 0.25    | 0       |
| θ6 ∪ θ8         | 0       | 0.75    | 0       | 0.25    |
| θ4 ∪ θ8         | 0       | 0       | 0.75    | 0       |
| It              | 0       | 0.25    | 0       | 0.75    |

Table 68: Corresponding quantitative inputs.

Applying PCR5 and PCR6 fusion rules, one gets the results given in Table 69 for quantitative and approxi-