- with PCR6: ∆(θ6 ∪ θ7 ∪ θ8) = 0.**130503**
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**869497**, 1]
P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 0.**130503]**
and when considering θ7 ∪ θ8
- with PCR5: ∆(θ7 ∪ θ8) = 0.**1537**
P(θ7 ∪ θ8) ∈ [0.2730, 0.**4267]** P(θ7 ∪ θ8) ∈ [0.5733, 0.**7270]**
- with PCR6: ∆(θ7 ∪ θ8) = 0.**1537**
P(θ7 ∪ θ8) ∈ [0.2730, 0.**4267]**
P(θ7 ∪ θ8) ∈ [0.5733, 0.**7270]**
and when considering θ8 **only**
- with PCR5: ∆(θ8) = 0.**071335**
P(θ8) ∈ [0.2730, 0.**344335]** P(
¯θ8) ∈ [0.655665, 0.**7270]**
- with PCR6: ∆(θ8) = 0.**076345**
P(θ8) ∈ [0.2730, 0.**349345]**
P(
¯θ8) ∈ [0.650655, 0.**7270]**
Based on DSmP transformation, one gets a pretty low probability on θ8 and on θ7 ∪ θ8**, but a very high**
probability on the most prudent decision-support fypothesis θ6 ∪ θ7 ∪ θ8 **because**
DSmPǫ,P CR5(θ6 ∪ θ7 ∪ θ8) = 0.**9992**
DSmPǫ,P CR6(θ6 ∪ θ7 ∪ θ8) = 0.**9993**
DSmPǫ,P CR5(θ7 ∪ θ8) = 0.**3168** DSmPǫ,P CR6(θ7 ∪ θ8) = 0.**3180**
DSmPǫ,P CR5(θ8) = 0.**3166** DSmPǫ,P CR6(θ8) = 0.**3178**

- Answer to Q1: **Based on these results, one sees**
that the decision based either on the max of credibility, the max of plausibility or the max of DSmP
considering both cases θ8 or θ7 ∪ θ8 **is to: NOT**
Evacuate the building B**, whereas the most prudent/cautious strategy suggests the opposite, i.e.**
the evacuation of the building B.
Let's examine the results of fusion systems m0 ⊕ m2 and m0 ⊕m1⊕m3 **corresponding to the input Table 28.** Naturally, one gets same results for the fusion m0 ⊕ m2 as in Example 3 and for the fusion m0 ⊕ m1 ⊕ m3 one gets:

| focal element   | mP CR5(.)   | mP CR6(.)   |
|-----------------|-------------|-------------|
| θ8              | 0.091       | 0.091       |
| θ4 ∪ θ8         | 0.009       | 0.009       |
| θ6 ∪ θ8         | 0.819       | 0.819       |
| It              | 0.081       | 0.081       |

Table 32: Result of m0 ⊕ m1 ⊕ m3.

| Singletons   | DSmPǫ,P CR5(.)   | DSmPǫ,P CR6(.)   |
|--------------|------------------|------------------|
| θ1           | 0.0008           | 0.0008           |
| θ2           | 0.0008           | 0.0008           |
| θ3           | 0.0008           | 0.0008           |
| θ4           | 0.0009           | 0.0009           |
| θ5           | 0.0008           | 0.0008           |
| θ6           | 0.0096           | 0.0096           |
| θ7           | 0.0008           | 0.0008           |
| θ8           | 0.9854           | 0.9854           |

Table 33: **DSmP**ǫ of m0 ⊕ m1 ⊕ m3.

| Singletons   | BetPP CR5(.)   | BetPP CR6(.)   |
|--------------|----------------|----------------|
| θ1           | 0.0101         | 0.0101         |
| θ2           | 0.0101         | 0.0101         |
| θ3           | 0.0101         | 0.0101         |
| θ4           | 0.0146         | 0.0146         |
| θ5           | 0.0101         | 0.0101         |
| θ6           | 0.4196         | 0.4196         |
| θ7           | 0.0101         | 0.0101         |
| θ8           | 0.5151         | 0.5151         |

As in Example 3, based on m0⊕m2 **fusion result, one**
gets a large imprecision on evaluation of probabilities of decision-support hypotheses since for θ6∪θ7∪θ8**, one** has ∆02(θ6 ∪ θ7 ∪ θ8**) = 1 and**
P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 1]
P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 1]
for θ7 ∪ θ8, one has also ∆02(θ7 ∪ θ8**) = 1 with**
P(θ7 ∪ θ8) ∈ [0, 1] P(θ7 ∪ θ8) ∈ [0, 1]
and for θ8, one gets ∆02(θ8) = 0.**30875 with**
P(θ8) ∈ [0, 0.**30875]** P(
¯θ8) ∈ [0.**69125**, 1]
One sees that it is impossible to take a decision when considering only θ6 ∪ θ7 ∪ θ8 or θ7 ∪ θ8 **because of full**
imprecision of the corresponding probabilities. Based on max of Bel or max of Pl criteria on θ8 **the decision** using m0 ⊕ m2 **is to NOT evacuate the building** B. According to Tables 23-24, an ambiguity appears in decision-making between θ8 and θ4 **since they have the** same DSmP (or BetP) values.