
## 5.3 Examples For Dsmp And Betp

The examples briefly presented here are detailed in [36] which includes also additional results based on Cuzzolin's and Sudano's transformations.

## - With Shafer'S Model And A Non-Bayesian Mass

Let's consider the frame Θ = {**A, B**} and let's assume Shafer's model and the non-Bayesian mass (more precisely the simple support mass) given in Table 6. We summarize in Table 7, the results obtained with DSmP
and BetP. One sees that P IC(**DSmP**ǫ→0) is maximum among all PIC values.

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

Table 6: Quantitative inputs.

| A              | B      | P IC(.)   |        |
|----------------|--------|-----------|--------|
| BetP(.)        | 0.7000 | 0.3000    | 0.1187 |
| DSmPǫ=0.001(.) | 0.9985 | 0.0015    | 0.9838 |
| DSmPǫ=0(.)     | 1      | 0         | 1      |

The best result is an *adequate probability*, not *the biggest PIC* in this case. This is because P(B) deserves to receive some mass from m(A∪B), so the most correct result is done by DSmPǫ=0.001 in Table 7 (of course we can choose any other very small positive value for ǫ if we want). Always when a singleton whose mass is zero, but it is involved in an ignorance whose mass is not zero, then ǫ (in **DSmP** formula (22)) should be taken different from zero.

## - With A Hybrid Dsm Model

Let's consider the frame Θ = {**A, B, C**} and let's consider the hybrid DSm model in which all intersections of elements of Θ are empty, but A ∩ B corresponding to figure 4. In this case, GΘ reduces to 9 elements
{∅, A ∩ B, A, B, C, A ∪ B, A ∪ C, B ∪ **C, A** ∪ B ∪ C}. The input masses of focal elements are given by m(A ∩ B) = 0.20, m(A) = 0.10, m(C) = 0.20, m(A ∪ B) = 0.30, m(A ∪ C) = 0.10, and m(A ∪ B ∪ C) = 0.10 and given in the Table 8.

![0_image_1.png](0_image_1.png)

![0_image_2.png](0_image_2.png)

