where < α, γ > is the scalar product of α = (αi)i∈{1**,...,M**}
and γ = (γi)i∈{1**,...,M**} with:

$$\gamma_{i}=\frac{m_{i}(X)}{m_{i}(X)+\sum_{j=1}^{M-1}m_{\sigma_{i}(j)}(Y_{\sigma_{i}(j)})},\tag{30}$$

where γi(X, Yσi(1)**, ..., Y**σi(M−1)) is noted γi for notations.

With this last version of the rule, for αi given by the equation (27), we obtain on our illustrative example λ =
36 13 when the experts 1, 2 and 3 say respectively A, B, and A∪C (the conflict is 0.21), λ =
16 5 when the conflict is 0.14 and λ = 56 17 when the conflict is 0.09. Thus, the masses are given by:

mDPCR(A) = 0.14 + 0.21 + 0.21 7 18 1 6 36 13 + 0.14 7 16 1 6 16 5 ≃ 0.420, mDPCR(B) = 0.06 + 0.14 5 16 1 6 16 5 + 0.09 5 14 1 6 56 17 ≃ 0.101, mDPCR(A ∪ C) = 0.09 + 0.21 6 18 1 6 36 13 + 0.09 6 14 1 6 56 17 ≃ 0.143, mDPCR(A ∪ B ∪ C) = 0.21 2 3 = 0.14 mDPCR(Θ) = 0.06 + 0.14 4 16 1 3 16 5 + 0.09 3 14 1 3 56 17 +0.14 13 + 0.09 1 3 ≃ 0.196. This last version allows to consider a kind of degree of conflict (Yσi
(a degree of pair of non-conflict), but this degree is not so easy to introduce in the combination rule.

## C. A Mixed Discounting Conflict Repartition Rule

From both new rules, the mixed rule (22) and the discounting PCR (24), we propose a combination of these rules, given for two basic belief assignments m1 and m2 and for all X ∈ 2 Θ, X 6= ∅ by:

$$\begin{array}{c}\mbox{$m_{\rm MDpCR}(X)=$}\sum_{Y_{1}\sqcup Y_{2}=X,$}\\ \mbox{$Y_{1}\cap Y_{2}\neq\emptyset$}\\ +\sum_{Y_{1}\cap Y_{2}=X,$}\\ \mbox{$Y_{1}\cap Y_{2}=X,$}\\ +\sum_{Y_{1}\cap Y_{2}\neq\emptyset$}\\ +\sum_{Y\in\mathbb{Z}^{\oplus},\quad\alpha\left(\frac{m_{1}(X)^{2}m_{2}(Y)}{m_{1}(X)+m_{2}(Y)}+\frac{m_{2}(X)^{2}m_{1}(Y)}{m_{2}(X)+m_{1}(Y)}\right),\\ \mbox{$X\cap Y=\emptyset$}\\ +\sum_{Y_{1}\cup Y_{2}=X}\\ \mbox{$Y_{1}\cap Y_{2}=\emptyset$}\end{array}\tag{31}$$

α can be given by the equation (26) and δ by the equation
(20) or (21). The weights are taken to get a kind of continuity between the mixed and DPCR rules. Actually, when the intersection of the responses is almost empty but not empty we use the mixed rule and when this intersection is empty we chose the **DPCR** rule. In the first case all the mass is transfered on the union and in the second one it will be the same according to the partial conflict. Indeed, α = 0 if the intersection is not empty and δ = 1 if the intersection is empty.

We can also introduce αi given by the equation (27), and this continuity is conserved.

This rule is given in a general case for M experts, for all

X ∈ 2 Θ, X 6= ∅ by: δY M mMDPCR(X) = X j=1 mj (Yj ) Y1∪...∪YM=X, Y1∩...∩YM6=∅ Y1∩...∩YM=X, Y1∩...∩YM6=∅ (1 − δ)Y M +X j=1 mj (Yj ) +X M i=1 mi(X) 2 (32) α   mi(X)+ M X−1 j=1 mσi(j)(Yσi(j))   M Y−1 j=1 mσi(j)(Yσi(j)) X M−1 ∩ k=1 Yσi (k)∩X=∅ (Yσi (1),...,Yσi (M−1))∈(2Θ)M−1 Y1∪...∪YM=X Y1∩...∩YM=∅ (1 − α)Y M +X j=1 mj (Yj ), where Yj ∈ 2 Θ is the response of the expert j, mj (Yj ) the
associated belief function and σiis given by (13). This formula could seem difficult to understand, but we can implement it easily as shown in appendix VI.

If we take again the previous example with δ given by the equation (20), there is no difference with the **DPCR**. If δ is calculated by the equation (21), the only difference pertains to the mass 0.09 coming from the responses of the three experts:
Θ, Θ and A∪C. This mass is transfered on A∪C (0.06) and on Θ (0.03).

IV. DISCUSSION: TOWARD A MORE GENERAL RULE
The rules presented in the previous section, propose a repartition of the masses giving a partial conflict only (when at most two experts are in discord) and do not take heed of the level of imprecision of the responses of the experts (the nonspecificity of the responses). The imprecision of the responses of each expert is only considered by the mixed and MDPCR rules when there is no conflict between the experts.

In the mixed rule, if the intersection of the responses of the experts is empty, the best way is not necessarily to transfer the