Based on m0 ⊕ m1 ⊕ m3 **fusion result, one gets**
∆013(θ6 ∪ θ7 ∪ θ8) = 0.09 for θ6 ∪ θ7 ∪ θ8 **with**

$$91,1]$$
$\square$
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.91, 1] P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 0.09]
and ∆013(θ7 ∪ θ8) = 0.9090 for θ7 ∪ θ8 **with**
P(θ7 ∪ θ8) ∈ [0.091, 1]
P(θ7 ∪ θ8) ∈ [0, 0.**9090]**
and ∆013(θ8) = 0.9090 for only θ8 **with**
P(θ8) ∈ [0.091, 1]
P(
¯θ8) ∈ [0, 0.**9090]**
Based on max of Bel or max of Pl criteria on either θ8, θ7∪θ8 or θ6∪θ7∪θ8 the decision using m0⊕m1⊕m3 **must**
be the evacuation of the building B**. Same decision is** drawn using DSmP or BetP results according to Tables 33 and 34.

- Answer to Q2: **Similar remarks and conclusions**
to those given in Example 3 held also for Example 4, i.e. it is better to adopt the most prudent strategy (i.e. to consider θ6 ∪ θ7 ∪ θ8 **as decisionsupport hypothesis) and to trust the most precise**
fusion system with respect this hypothesis, which is in this example the subsystem m0 ⊕ m1 ⊕ m3. Based only on m0 ⊕ m1 ⊕ m3 **the final decision**
will be to evacuate the building B **when one has in**
hands such highly uncertain prior information m0.

## 3.3 Impact Of No Prior Information

Example 5**: Let's examine the result of the fusion**
process if one doesn't include5**the prior information**
m0(.**) and if we combine directly only the three sources** m1 ⊕ m2 ⊕ m3 **altogether with PCR5 or PCR6.**

| focal element   | m1(.)   | m2(.)   | m3(.)   |
|-----------------|---------|---------|---------|
| θ4 ∪ θ8         | 0       | 0.3     | 0       |
| θ6 ∪ θ8         | 0.75    | 0       | 0.25    |
| θ4 ∪ θ8         | 0       | 0.7     | 0       |
| It              | 0.25    | 0       | 0.75    |

Table 35: Quantitative inputs of VBIED problem.

| focal element               | mP CR5(.)   | mP CR6(.)   |
|-----------------------------|-------------|-------------|
| θ6                          | 0.56875     | 0.56875     |
| θ1 ∪ θ2 ∪ θ3 ∪ θ5 ∪ θ6 ∪ θ7 | 0.13125     | 0.13125     |
| θ8                          | 0.24375     | 0.24375     |
| θ4 ∪ θ8                     | 0.05625     | 0.05625     |

Table 36: Result of m1 ⊕ m2 ⊕ m3 **for Table 35.**

$\mathrm{i}\mathrm{t}\mathrm{t}\mathrm{h}$. 
Table 37: DSmPǫ of m1 ⊕ m2 ⊕ m3 **for Table 35.**
Table 38: BetP of m1 ⊕ m2 ⊕ m3 **for Table 35.**

| Singletons   | DSmPǫ,P CR5(.)   | DSmPǫ,P CR6(.)   |
|--------------|------------------|------------------|
| θ1           | 0.0002           | 0.0002           |
| θ2           | 0.0002           | 0.0002           |
| θ3           | 0.0002           | 0.0002           |
| θ4           | 0.0002           | 0.0002           |
| θ5           | 0.0002           | 0.0002           |
| θ6           | 0.6989           | 0.6989           |
| θ7           | 0.0002           | 0.0002           |
| θ8           | 0.2998           | 0.2998           |

One gets ∆(θ6 ∪ θ7 ∪ θ8) = 0.1875 for θ6 ∪ θ7 ∪ θ8 **with**

| Singletons   | BetPP CR5(.)   | BetPP CR6(.)   |
|--------------|----------------|----------------|
| θ1           | 0.0219         | 0.0219         |
| θ2           | 0.0219         | 0.0219         |
| θ3           | 0.0219         | 0.0219         |
| θ4           | 0.0281         | 0.0281         |
| θ5           | 0.0219         | 0.0219         |
| θ6           | 0.5906         | 0.5906         |
| θ7           | 0.0219         | 0.0219         |
| θ8           | 0.2719         | 0.2719         |

$\pi=\pi$. 
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**8125**, 1]

$$P({\overline{{\theta_{6}\cup\theta_{7}\cup\theta_{8}}}})\in[0,0.1875]$$

for θ7 ∪ θ8, one has also ∆(θ7 ∪ θ8) = 0.**1875 with**
P(θ7 ∪ θ8) ∈ [0.24375, 0.**43125]**

$P(\overline{\theta_7\cup\theta_8})\in[0.56875,0.75625]$. 
and for θ8, one gets ∆(θ8) = 0.**05625 with**
P(θ8) ∈ [0.24375, 0.3], P(
¯θ8) ∈ [0.7, 0.**75625]**
The result presented in Table 36 is obviously the same as the one we obtain by combining the sources m0 ⊕
m1 ⊕ m2 ⊕ m3 altogether when taking m0(.**) as the**
vacuous belief assignment, i.e. when m0(It**) = 1.**

- Answer to Q1: **Based on results of Tables 36-38**
the decision based on max of belief, max of plausibility on either θ8 or θ7 ∪ θ8 **is to NOT evacuate**
building B**. Same conclusions is obtained when analyzing values of DSmP or BetP of** θ8 or θ7 ∪ θ8.

However, if we adopt the most prudent strategy based on decision-support hypothesis θ6 ∪ θ7 ∪ θ8 the decision will be to evacuate the building B
since DSmP(θ6 ∪ θ7 ∪ θ8) = 0.**9989. So we see the** strong impact of the miss of prior information in the decision-making support process (by comparison between Example 1 and this example) when adopting more risky strategies for decision-making based either on θ7 ∪ θ8 or on θ8 **only.**