case, one gets:

10
$$m_{T B M}(\varnothing)=m_{\land}(A\cap B)=13/36$$
$m_{TBM}(A)=13/36$  $m_{TBM}(B)=8/36$  $m_{TBM}(A\cup B)=2/36$

## - Yager'S Rule [32]–[34]:

Yager admits that in case of high conflict Dempster's rule provides counter-intuitive results. Thus, k plays the role of an absolute discounting term added to the weight of ignorance. The commutative and quasi-associative4 Yager's rule is given by mY (∅**) = 0** and ∀A ∈ GΘ **\ {∅}** by

$$m_{Y}(A)=m_{\land}(A)$$

$$m_{Y}(\Theta)=m_{\wedge}(\Theta)+m_{\wedge}(\varnothing)$$
$$(20)$$

Example 3: Let's consider the 2D frame and quantitative masses as given in example 1 and assume Shafer's model (*i.e.*
A ∩ B = ∅), then the conflicting quantitative mass k = m∧(A ∩ B**) = 13**/36 is transferred to total ignorance A ∪ B. One thus gets:

$$m_{Y}(A)=13/36$$
$m_{Y}(B)=8/36$  $m_{Y}(A\cup B)=(2/36)+(13/36)=15/36$

## - Dubois & Prade'S Rule [5]:

This rule supposes that the two sources are reliable when they are not in conflict and at least one of them is right when a conflict occurs. Then if one believes that a value is in a set X while the other believes that this value is in a set Y , the truth lies in X ∩Y as long X ∩Y 6= ∅. If X ∩Y = ∅, then the truth lies in X ∪Y . According to this principle, the commutative and quasi-associative Dubois & Prade hybrid rule of combination, which is a reasonable trade-off between precision and reliability, is defined by mDP (∅**) = 0** and ∀A ∈ GΘ **\ {∅}** by

$$m_{DP}(A)=m_{\wedge}(A)+\sum_{\begin{subarray}{c}X,Y\in\mathcal{G}^{n}\\ Y\cup Y=\emptyset\\ X(Y)=\emptyset\end{subarray}}m_{1}(X)m_{2}(Y)\tag{21}$$

In Dubois & Prade's rule, the conflicting information is considered more precisely than in Dempster's or Yager's rules since all partial conflicts involved the total conflict are taken into account separately through (21).

The repartition of the conflict is very important because of the non-idempotency of the rules (except the Denœux' rule [4] that can be applied when the dependency between experts is high) and due to the responses of the experts that can be conflicting. Hence, we have defined the auto-conflict [16] in order to quantify the intrinsic conflict of a mass and the distribution of the conflict according to the number of experts.