Based on m0 ⊕m1 ⊕m3 **fusion results given in Tables**
25-27, one gets for θ6∪θ7∪θ8 the imprecision ∆013(θ6∪
θ7 ∪ θ8) = 0.**1875 with**
P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**8125**, 1]
P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 0.**1875]**
for θ7 ∪ θ8, one gets ∆013(θ7 ∪ θ8) = 0.**91875 with**
P(θ7 ∪ θ8) ∈ [0.**08125**, 1] P(θ7 ∪ θ8) ∈ [0, 0.**91875]**
and for θ8, one gets ∆013(θ8) = 0.**91875 with**
P(θ8) ∈ [0.**08125**, 1] P(
¯θ8) ∈ [0, 0.**91875]**
Based on max of Bel or max of Pl criteria, the decision using m0⊕m1⊕m3 **is the evacuation of the building**
B**. Same decision is drawn when using DSmP or BetP**
results according to Tables 26 and 27. With this uncertain prior information, it is worth to note that the precision on the result obtained with m0 ⊕ m1 ⊕ m3 is better than with m0⊕m2 **when considering (in cautious** strategy) the decision-support hypotheses θ6 ∪ θ7 ∪ θ8 or θ7 ∪θ8 since ∆013(θ6 ∪θ7 ∪θ8) < ∆02(θ6 ∪θ7 ∪θ8**), or**
∆013(θ7 ∪ θ8) < ∆02(θ7 ∪ θ8**). However, if a more optimistic/risky strategy is used when considering only** θ8 as decision-support hypothesis, it is preferable to choose the subsystem m0 ⊕ m2 because ∆02(θ8) < ∆013(θ8). However, one sees that globally 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: **The answer of question Q2 is**
not easy because it depends both on the criterion (precision or PIC) and on the decision-support hypothesis we choose. Based on precision criterion and taking the optimistic point of view using only θ8, it is better to trust m0 ⊕ m2 fusion system since ∆02(θ8**) = ∆**02(
¯θ8) = 0.**30875 whereas**
∆013(θ8) = ∆013(
¯θ8) = 0.**9187. In such case, one**
should NOT evacuate the building B**. If we consider that is better to trust result of** m0 ⊕ m1 ⊕ m3 fusion system because it is more informative than m0 ⊕ m2 **then the decision should be to evacuate** the building B**. If we take a more prudent point of** view in considering as decision-support hypotheses either θ6 ∪θ7 ∪θ8 or θ7 ∪θ8**, then the final decision**
taken according to the (most precise and informative) subsystem m0 ⊕ m1 ⊕ m3 **is to evacuate the**
building B. So the main open question is what solution to choose for selecting either m0⊕m2 or m0⊕m1⊕m3 fusion system ? In authors opinion, in such case it seems better to base our choice on the precision Page 11
level of information one has really in hands (rather than the PIC value which is always related to some ad-hoc probabilistic transformation) and in adopting the most prudent strategy. Therefore for this example, the final decision must be done according to m0 ⊕ m1 ⊕ m3**, i.e. evacuate the building** B.

Example 4**: Let's modify a bit the previous input Table 18 and take higher belief for sources 1 and 3 as**

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

Table 28: Quantitative inputs of VBIED problem.

focal element mP CR5(.) m**P CR**6(.) θ6 0.573300 **0.573300**

θ1 ∪ θ2 ∪ θ3 ∪ θ5 ∪ θ6 ∪ θ7 0.082365 **0.077355**

θ8 0.273000 **0.273000**

θ4 ∪ θ8 0.030666 **0.029951**

θ6 ∪ θ8 0.020334 **0.023197**

It 0.020334 **0.023197**

Table 29: Result of m0 ⊕ m1 ⊕ m2 ⊕ m3 **for Table 28.**
Table 30: DSmPǫ of m0 ⊕ m1 ⊕ m2 ⊕ m3 **for Table 28.**
Table 31: BetP of m0 ⊕ m1 ⊕ m2 ⊕ m3 **for Table 28.**

| Singletons   | DSmPǫ,P CR5(.)   | DSmPǫ,P CR6(.)   |
|--------------|------------------|------------------|
| θ1           | 0.0002           | 0.0002           |
| θ2           | 0.0002           | 0.0002           |
| θ3           | 0.0002           | 0.0002           |
| θ4           | 0.0001           | 0.0001           |
| θ5           | 0.0002           | 0.0002           |
| θ6           | 0.6824           | 0.6813           |
| θ7           | 0.0002           | 0.0002           |
| θ8           | 0.3166           | 0.3178           |

Therefore, one gets when considering θ6 ∪ θ7 ∪ θ8

| Singletons   | BetPP CR5(.)   | BetPP CR6(.)   |
|--------------|----------------|----------------|
| θ1           | 0.0163         | 0.0158         |
| θ2           | 0.0163         | 0.0158         |
| θ3           | 0.0163         | 0.0158         |
| θ4           | 0.0179         | 0.0179         |
| θ5           | 0.0163         | 0.0158         |
| θ6           | 0.5997         | 0.6007         |
| θ7           | 0.0163         | 0.0158         |
| θ8           | 0.3010         | 0.3025         |

- with PCR5: ∆(θ6 ∪ θ7 ∪ θ8) = 0.**133366**

P(θ6 ∪ θ7 ∪ θ8) ∈ [0.**866634**, 1]
P(θ6 ∪ θ7 ∪ θ8) ∈ [0, 0.**133366]**