Here are the results obtained from Dempster's rule, DSmH and PCR5:

A B A ∪ B

mDS 0.512 0.146 0.342 m**DSmH** 0.420 0.120 0.460 m**P CR**5 0.540 0.180 0.280

- **Example 2**: Let's modify example 1 and consider The conflicting mass k12 = m∩(A ∩ B) as well as the distribution coefficients for the PCR5 remains the same as in the previous example but one gets now
- **Example 3**: Let's modify example 2 and consider The conflicting mass k12 = 0.24 = m1(A)m2(B) + m1(B)m2(A) = 0.24 is now different from previous examples, which means that m2(A) = 0.2 and m1(B) = 0.3 did make an impact on the conflict. Therefore A and B are the only focal elements involved in the conflict and thus only A and B
deserve a part of the conflicting mass. PCR5 redistributes the partial conflicting mass 0.18 to A and B
proportionally with the masses m1(A) and m2(B) and also the partial conflicting mass 0.06 to A and B
proportionally with the masses m2(A) and m1(B). After all derivations (see [13] for details), one finally gets:

A B A ∪ B

mDS 0.579 0.355 0.066 m**DSmH** 0.440 0.270 0.290 m**P CR**5 0.584 0.366 0.050

| A     | B    | A ∪ B   |      |
|-------|------|---------|------|
| m1(.) | 0.6  | 0       | 0.4  |
| m2(.) | 0.2  | 0.3     | 0.5  |
| m∩(.) | 0.50 | 0.12    | 0.20 |

One clearly sees that mDS(A ∪ B) gets some mass from the conflicting mass although A ∪ B does not deserve any part of the conflicting mass (according to PCR5 hypothesis) since A ∪ B is not involved in the conflict (only A and B are involved in the conflicting mass). Dempster's rule appears to us less exact than PCR5 and Inagaki's rules [15]. It can be showed [13] that Inagaki's fusion rule (with an optimal choice of tuning parameters) can become in some cases very close to PCR5 but upon our opinion PCR5 result is more exact (at least less ad-hoc than Inagaki's one).

| A      | B     | A ∪ B   |       |
|--------|-------|---------|-------|
| mDS    | 0.609 | 0.146   | 0.231 |
| mDSmH  | 0.500 | 0.120   | 0.380 |
| mP CR5 | 0.620 | 0.180   | 0.200 |

- **Example 4 (A more concrete example)**: Three people, John (J), George (G), and David (D) are suspects to a murder. So the frame of discernment is Θ , {**J, G, D**}. Two sources m1(.) and m2(.)
(witnesses) provide the following information:

| A     | B    | A ∪ B   |      |
|-------|------|---------|------|
| m1(.) | 0.6  | 0.3     | 0.1  |
| m2(.) | 0.2  | 0.3     | 0.5  |
| m∩(.) | 0.44 | 0.27    | 0.05 |

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