range of P(θ6 ∪ θ7 ∪ θ8) or P(θ7 ∪ θ8**). The decision** using m0 ⊕ m2 (i.e. with prior information m0 and ANPR system m2**) based only on supporting hypothesis** θ8 should be to NOT evacuate the building B**. Same**
decision would be taken based on DSmP or BetP values.

focal element mP CR5(.) m**P CR**6(.)

![0_image_0.png](0_image_0.png)

![0_image_1.png](0_image_1.png)

θ8 0.8125 **0.8125**
θ4 ∪ θ8 0.1875 **0.1875**
Table 8: Result of m0 ⊕ m1 ⊕ m3.

| Singletons   | DSmPǫ,P CR5(.)   | DSmPǫ,P CR6(.)   |
|--------------|------------------|------------------|
| θ1           | 0                | 0                |
| θ2           | 0                | 0                |
| θ3           | 0                | 0                |
| θ4           | 0.0002           | 0.0002           |
| θ5           | 0                | 0                |
| θ6           | 0                | 0                |
| θ7           | 0                | 0                |
| θ8           | 0.9998           | 0.9998           |

Table 9: **DSmP**ǫ of m0 ⊕ m1 ⊕ m3.

| Singletons   | BetPP CR5(.)   | BetPP CR6(.)   |
|--------------|----------------|----------------|
| θ1           | 0              | 0              |
| θ2           | 0              | 0              |
| θ3           | 0              | 0              |
| θ4           | 0.09375        | 0.09375        |
| θ5           | 0              | 0              |
| θ6           | 0              | 0              |
| θ7           | 0              | 0              |
| θ8           | 0.90625        | 0.90625        |

Table 10: **BetP** of m0 ⊕ m1 ⊕ m3.

Based on m0 ⊕ m1 ⊕ m3 **fusion result, one gets**
∆013(θ6 ∪ θ7 ∪ θ8) = 0.**1875**
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**8125**, 1]

$$P({\overline{{\theta_{6}\cup\theta_{7}\cup\theta_{8}}}})\in[0,0.1875]$$
$$25,1],\qquad P({\overline{{\theta_{7}\cup\theta_{8}}}})\in[0,0.1875]$$
Page 7
but also

$$\theta_{7}\cup\theta_{8})\in[0.8]$$
P(θ7 ∪ θ8) ∈ [0.8125, 1], P(θ7 ∪ θ8) ∈ [0, 0.**1875]**
and

$$P(\theta_{8})\in[0.8125,1],\qquad P(\bar{\theta}_{8})\in[0,0.1875]$$

Based on max of Bel or max of Pl criteria, the decision using m0⊕m1⊕m3 **(i.e. with prior information** m0 and both analysts) is to evacuate the building B**. The** same decision is taken based on DSmP or BetP values.

It is worth to note that the precision on the result obtained with m0 ⊕ m1 ⊕ m3 **is much better than with**
m0 ⊕ m2 since ∆013(θ6 ∪ θ7 ∪ θ8) < ∆02(θ6 ∪ θ7 ∪ θ8), or ∆013(θ7 ∪ θ8) < ∆02(θ7 ∪ θ8**). Moreover it is easy to**
verify that m0 ⊕ m1 ⊕ m3 fusion system is more informative than m0 ⊕ m2 **fusion system because Shannon**
entropy of DSmP of m0⊕m2 **is much bigger than Shannon entropy of DSmP of** m0 ⊕ m1 ⊕ m3.

- Answer to Q2: **Since the information obtained**
by the fusion m0 ⊕ m2 **is less informative and less** precise than the information obtained with the fusion m0 ⊕ m1 ⊕ m3**, it is better to choose and**
to trust the fusion system m0 ⊕ m1 ⊕ m3 **rather** than m0 ⊕ m2**. Based on this choice, the final**
decision will be to evacuate the building B **which** is consistent with answer to question Q1.
Example 2**: Let's modify a bit the previous Table 1**
and take higher belief for sources 1 and 3 as Table 11: Quantitative inputs of VBIED problem.

| focal element   | m0(.)   | m1(.)   | m2(.)   | m3(.)   |
|-----------------|---------|---------|---------|---------|
| θ4 ∪ θ8         | 1       | 0       | 0.3     | 0       |
| θ6 ∪ θ8         | 0       | 0.9     | 0       | 0.1     |
| θ4 ∪ θ8         | 0       | 0       | 0.7     | 0       |
| It              | 0       | 0.1     | 0       | 0.9     |

The results of the fusion m0 ⊕ m1 ⊕ m2 ⊕ m3 **using** PCR5 and PCR6 and the corresponding DSmP values are given in tables 12-13.

| focal element               | mP CR5(.)   | mP CR6(.)   |
|-----------------------------|-------------|-------------|
| θ1 ∪ θ2 ∪ θ3 ∪ θ5 ∪ θ6 ∪ θ7 | 0.16525     | 0.14865     |
| θ8                          | 0.27300     | 0.27300     |
| θ4 ∪ θ8                     | 0.26307     | 0.23935     |
| θ6 ∪ θ8                     | 0.14934     | 0.16950     |
| It                          | 0.14934     | 0.16950     |

Table 12: Results of m0 ⊕ m1 ⊕ m2 ⊕ m3 **for Table 11.**

| Singletons   | DSmPǫ,P CR5(.)   | DSmPǫ,P CR6(.)   |
|--------------|------------------|------------------|
| θ1           | 0.0281           | 0.0254           |
| θ2           | 0.0281           | 0.0254           |
| θ3           | 0.0281           | 0.0254           |
| θ4           | 0.0015           | 0.0015           |
| θ5           | 0.0281           | 0.0254           |
| θ6           | 0.0286           | 0.0260           |
| θ7           | 0.0281           | 0.0254           |
| θ8           | 0.8294           | 0.8455           |

Table 13: DSmPǫ of m0 ⊕ m1 ⊕ m2 ⊕ m3 **for Table 11.**
From fusion result of Table 12, one gets when considering θ6 ∪ θ7 ∪ θ8
- with PCR5: ∆(θ6 ∪ θ7 ∪ θ8) = 0.**57766**
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**42234**, 1]

$$P({\overline{{\theta_{6}\cup\theta_{7}\cup\theta_{8}}}})\in[0,57766]$$
