Let's compare now the source m2 **with respect to the**
m1⊕m3 **fusion system when no prior information** m0 is used. Naturally, there is no need to fusion m2 **since we**
consider it alone. One has ∆2(θ6 ∪ θ7 ∪ θ8**) = ∆**2(θ7 ∪
θ8) = 1 (i.e. the full imprecision on P(θ6 ∪ θ7 ∪ θ8**) and**
on P(θ7 ∪ θ8)) whereas ∆2(θ8) = 0.**3 with**

## P(Θ8) ∈ [0, 0.3], P( ¯Θ8) ∈ [0.7, 1]

DSmP and BetP of m2(.**) are the same since there is no** singleton as focal element for m2(.**) - see Table 39.**

| Singletons   | DSmPǫ,P CR5(.)   | BetP(.)   |
|--------------|------------------|-----------|
| θ1           | 0.1167           | 0.1167    |
| θ2           | 0.1167           | 0.1167    |
| θ3           | 0.1167           | 0.1167    |
| θ4           | 0.1500           | 0.1500    |
| θ5           | 0.1167           | 0.1167    |
| θ6           | 0.1167           | 0.1167    |
| θ7           | 0.1167           | 0.1167    |
| θ8           | 0.1500           | 0.1500    |

Table 39: DSmPǫ and **BetP** of m2.

Based on max of Bel or max of Pl criteria on θ8 (optimistic/risky strategy) the decision using m2 **(ANPR**
system alone) should be to NOT evacuate the building B**. No decision can be taken using decision-support** hypotheses θ6 ∪ θ7 ∪ θ8 or θ7 ∪ θ8**, nor on DSmP or** BetP values since there is an ambiguity between θ8 and θ4.

Now if we combine m1 with m3 **using PCR5 or**
PCR6 we get6**results given in Tables 40 and 41.**

focal element mP CR5(.) m**P CR**6(.)
θ6 ∪ θ8 0.8125 **0.8125**

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

Table 40: Result of m1 ⊕ m3.

| Singletons   | DSmPǫ,P CR5(.)   | DSmPǫ,P CR6(.)   |
|--------------|------------------|------------------|
| θ1           | 0.0234           | 0.0234           |
| θ2           | 0.0234           | 0.0234           |
| θ3           | 0.0234           | 0.0234           |
| θ4           | 0.0234           | 0.0234           |
| θ5           | 0.0234           | 0.0234           |
| θ6           | 0.4297           | 0.4297           |
| θ7           | 0.0234           | 0.0234           |
| θ8           | 0.4297           | 0.4297           |

The values of BetP(.) are same as those of **DSmP**(.)
because there is no singleton as focal element of m1 ⊕ m3.

Whence ∆13(θ6 ∪ θ7 ∪ θ8) = 0.**1875 with**

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

P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 0.**1875]**
and ∆13(θ7 ∪ θ8**) = 1 with**

$$P(\theta_{7}\cup\theta_{8})\in[0,1],\qquad P(\overline{\theta_{7}\cup\theta_{8}})\in[0,1]$$  and also $\Delta_{13}(\theta_{8})=1$ with  $$P(\theta_{8})\in[0,1],\qquad P(\bar{\theta}_{8})\in[0,1]$$

Based on max of Bel or max of Pl criteria on θ6∪θ7∪
θ8, the decision using m1 ⊕ m3 **must be the evacuation** of the building B**. Same decision must be drawn when** using DSmP results according to Table 41. No decision can be drawn based only on θ8 or on θ7 ∪ θ8 **because of** full imprecision on their corresponding probabilities.

- Answer to Q2: **Similar remarks and conclusions**
to those given in Example 3 held also for Example 5, i.e. it is better to trust the most precise source for the most prudent decision-support hypothesis, and to decide to evacuate the building B **if one** has no prior information rather than using only information based on APNR system.

Example 6**: It can be easily verified that the same** analysis, remarks and conclusions for Q1 and Q2 as for Example 5 also hold when considering the sources m1 and m3 **corresponding to the following input Table**
Table 42: Quantitative inputs of VBIED problem.

| focal element   | m1(.)   | m2(.)   | m3(.)   |
|-----------------|---------|---------|---------|
| θ4 ∪ θ8         | 0       | 0.3     | 0       |
| θ6 ∪ θ8         | 0.90    | 0       | 0.10    |
| θ4 ∪ θ8         | 0       | 0.7     | 0       |
| It              | 0.10    | 0       | 0.90    |

## 3.4 Impact Of Reliability Of Sources

The reliability of sources (when known) can be easily taken into using Shafer's classical discounting technique [5], p. 252, which consists in multiplying the masses of focal elements by the reliability factor α**, and transferring all the remaining discounted mass to the full**
ignorance Θ. When α < **1, such very simple reliability** discounting technique discounts all focal elements with the same factor α **and it increases the non specificity of** the discounted sources since the mass committed to the full ignorance always increases. When α **= 1, no reliability discounting occurs (the bba is kept unchanged).**
Mathematically, Shafer's discounting technique for taking into account the reliability factor α ∈ [0, **1] of a**