
| focal element   | mP CR5(.)   | mP CR6(.)   |
|-----------------|-------------|-------------|
| θ8              | 0.24375     | 0.24375     |
| θ4 ∪ θ8         | 0.36788     | 0.33034     |
| θ6 ∪ θ8         | 0.10552     | 0.14132     |
| θ4 ∪ θ8         | 0.21814     | 0.19186     |
| It              | 0.064701    | 0.092734    |

committed to partial ignorances, and it doesn't also increase the number of focal elements of the resulting bba contrariwise to the reliability discounting approach. Indeed in Table 53 one gets only 5 focal elements whereas one gets 6 focal elements with reliability discounting as shown in Table 44 of Example 7. The corresponding DSmP and BetP values of bba's given in Table 53 are summarized in Tables 54 and 55 .

| Singletons   | DSmPǫ,P CR5(.)   | DSmPǫ,P CR6(.)   |
|--------------|------------------|------------------|
| θ1           | 0.0366           | 0.0323           |
| θ2           | 0.0366           | 0.0323           |
| θ3           | 0.0366           | 0.0323           |
| θ4           | 0.0018           | 0.0017           |
| θ5           | 0.0366           | 0.0323           |
| θ6           | 0.0370           | 0.0329           |
| θ7           | 0.0366           | 0.0323           |
| θ8           | 0.7781           | 0.8036           |

Table 54: **DSmP**ǫ of mβ0 ⊕ mβ1 ⊕ mβ2 ⊕ mβ3.

| Singletons   | BetPP CR5(.)   | BetPP CR6(.)   |
|--------------|----------------|----------------|
| θ1           | 0.0444         | 0.0436         |
| θ2           | 0.0444         | 0.0436         |
| θ3           | 0.0444         | 0.0436         |
| θ4           | 0.1920         | 0.1768         |
| θ5           | 0.0444         | 0.0436         |
| θ6           | 0.0972         | 0.1142         |
| θ7           | 0.0444         | 0.0436         |
| θ8           | 0.4885         | 0.4912         |

Table 55: **BetP** of mβ0 ⊕ mβ1 ⊕ mβ2 ⊕ mβ3.

From the fusion result of Table 53, one gets when considering θ6 ∪ θ7 ∪ θ8
- with PCR5: ∆(θ6 ∪ θ7 ∪ θ8) = 0.**65073**
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**34927**, 1] P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 0.**65073]**
- with PCR6: ∆(θ6 ∪ θ7 ∪ θ8) = 0.**61493**
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**38507**, 1]
P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 0.**61493]**
and when considering θ7 ∪ θ8
- with PCR5: ∆(θ7 ∪ θ8) = 0.**75625**

$$\cos f$$

P(θ7 ∪ θ8) ∈ [0.**24375**, 1]

$\boxed{\sin\theta+\sin\theta}$. 
P(θ7 ∪ θ8) ∈ [0, 0.**75625]**
- with PCR6: ∆(θ7 ∪ θ8) = 0.**75625**

$\downarrow1$]. 
P(θ7 ∪ θ8) ∈ [0.**24375**, 1] P(θ7 ∪ θ8) ∈ [0, 0.**75625]**
and when considering θ8 **only**
- with PCR5: ∆(θ8) = 0.**53811**
P(θ8) ∈ [0.24375, 0.**78186]**
P(
¯θ8) ∈ [0.21814, 0.**75625]**
- with PCR6: ∆(θ8) = 0.**564393**
P(θ8) ∈ [0.24375, 0.**80814]** P(
¯θ8) ∈ [0.19186, 0.**75625]**
Using DSmP transformation, one gets a high probability in decision-support hypotheses because

DSmPǫ,P CR5(θ6 ∪ θ7 ∪ θ8) = 0.**8517**
$\mu_{\epsilon,PCR6}(\theta_{6}\cup\theta_{7}\cup\theta_{8})=0.8688$  $DSmP_{\epsilon,PCR5}(\theta_{7}\cup\theta_{8})=0.8147$  $DSmP_{\epsilon,PCR6}(\theta_{7}\cup\theta_{8})=0.8359$  $DSmP_{\epsilon,PCR5}(\theta_{8})=0.7781$  $DSmP_{\epsilon,PCR6}(\theta_{8})=0.8036$
- Answer to Q1: **Based on these results, one sees**
that the decision to take based either on max of Bel or max of Pl on θ6 ∪ θ7 ∪ θ8, on θ7 ∪ θ8 **or on**
θ8 **only, or also based on DSmP, is to evacuate the** building B.
To answer to the question Q2 for this Example 8, let's compute the fusion results of the fusion mβ0 ⊕mβ2 and mβ0 ⊕ mβ1 ⊕ mβ3 **using inputs given in Table 52.**
Because one has considered β0 = β2 **= 1, one does not**
actually discount sources m0 and m2 **and therefore the**
m0 ⊕ m2 **fusion results are already given in Tables 5**
and 6 of Example 1. Therefore based on max of Bel or max of Pl criteria on θ8 the decision using m0⊕m2 **is to** NOT evacuate the building B since P(θ8) ∈ [0, 0.**71176]** and P(
¯θ8) ∈ [0.28824, 1] and ∆02(θ8) = 0.**71176. Same**
decision would be taken based on DSmP values with the m0 ⊕ m2 **fusion sub-system.**
Let's now compute the fusion mβ0 ⊕ mβ1 ⊕ mβ3 **with**
the importance discounted sources mβ0=1 = m0, mβ1 and mβ3**. The fusion results are given in Tables 56, 57**
and 58.