
| δ1(., .) = δ(., .)   | A   | A ∪ B   | A ∪ B ∪ C   |
|----------------------|-----|---------|-------------|
| B                    | 1   | 0       | 0           |
| C                    | 1   | 1       | 0           |
| A ∪ C                | 0   | 1/2     | 0           |

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

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

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

| δ1(., .) = η(., .)     |     |       |           |
|------------------------|-----|-------|-----------|
| δ1(., .) = 1 − d(., .) | A   | A ∪ B | A ∪ B ∪ C |
| B                      | 1   | 1/2   | 2/3       |
| C                      | 1   | 1     | 2/3       |
| A ∪ C                  | 1/2 | 2/3   | 1/3       |
| A ∪ B ∪ C              | 2/3 | 1/3   | 0         |
| TABLE XI               |     |       |           |

Note that δ1(., .) = δ(**., .**) can be used when the experts are considered reliable. In this case, we consider the most precise response. With δ1(., .) = η(., .) or δ1(., .) = 1 − d(**., .**), we get the conjunctive rule only when the experts provide the same response, otherwise we consider the doubtful responses and we transfer the masses in proportion of the imprecision of the responses (given by the cardinality of the responses) on the part in agreement and on the partial ignorance.

## Example 11: (With A Hybrid Model)

Consider the same example with two (quantitative) experts providing m1(.) and m2(.) on the frame of discernment Θ =
{**A, B, C**} with the following integrity constraints: A ∩ B 6= ∅, A ∩ C = ∅ and B ∩ C = ∅ (which defines a so-called DSm-hybrid model [18]):
When taking δ1(., .) = δ(**., .**) according to (29), one obtains:
When taking δ1(., .) = η(**., .**) according to (30), one obtains:
When taking δ1(., .) = 1 − d(**., .**) according to (31), one obtains:
For more than two experts, say M > 2, if the intersection of the responses of the M experts is not empty, we can still transfer on the intersection and the union, and the equations (29) and (30) become:

$$\delta_{1}(Y_{1},...,Y_{M})=\delta(Y_{1},...,Y_{M})=1-\frac{\mathcal{C}(Y_{1}\cap...\cap Y_{M})}{\operatorname*{min}_{1\leq i\leq M}\mathcal{C}(Y_{i})},$$
$$(32)^{\frac{1}{2}}$$

C(Yi), (32)