mDPCR(A) = 0.14 + 0.21 + 0.21 · 7 18 · 1 3 + 0.14 · 7 16 · 2 3 ≃ 0.418 mDPCR(B) = 0.06 + 0.21 · 5 18 · 1 3 + 0.14 · 5 16 · 2 3 + 0.09 · 5 14 · 2 3 ≃ 0.130 mDPCR(A ∪ C) = 0.09 + 0.21 · 6 18 · 1 3 + 0.09 · 6 14 · 2 3 ≃ 0.139 mDPCR(A ∪ B ∪ C) = 0.21 · 2 3 = 0.140 mDPCR(A ∪ B ∪ C ∪ D) = 0.06 + 0.14 · 4 16 · 2 3 + 0.09 · 3 14 · 2 3 + 0.14 · 1 3 + 0.09 · 1 3 ≃ 0.173
We want to take account of the degree of conflict (or non-conflict) within each pair of expert differently for each element.

We can consider the non-conflict function given for each expert i by the number of experts not in conflict with i. Hence, we can choose αi(Y1**, ..., Y**M ) defined by the mapping of (GΘ)M onto 0, 1 M
with:

$$\alpha_{i}(Y_{1},...,Y_{M})=\frac{1}{M}-f_{i}(Y_{1},...,Y_{M})=\frac{\sum_{j=1,j\neq i}^{M}\mathds{1}_{\{Y_{j}\cap Y_{i}\neq\emptyset\}}}{M(M-1)}.$$

The discounting PCR rule (equation (37)) can be written for M experts, for all X ∈ GΘ, X 6= ∅ as:

$$(40)$$
M Y−1 j=1 mσi(j)(Yσi(j)) i=1 mi(X) 2 X M−1 ∩ k=1 Yσi(k) ∩ X = ∅ (Yσi(1), ..., Yσi(M−1)) ∈ (G Θ) M−1 αiλ   mi(X)+ M X−1 j=1 mσi(j)(Yσi(j))   mDPCR(X) = m∧(X) +X M +X Y1∪...∪YM=X Y1∩...∩YM≡∅ (1 −X M i=1 αi)Y M j=1 mj (Yj ), (41)
$$(41)$$
$$(42)$$

where αi(X, Yσi(1)**, ..., Y**σi(M−1)) is noted αi for notations convenience and λ depending on (X, Yσi(1)**, ..., Y**σi(M−1)), is chosen to obtain the normalization given by the equation (2). λ is given when αi 6= 0, ∀i ∈ {1**, ..., M**} by:

$$\lambda=\frac{\sum_{i=1}^{M}\alpha_{i}}{<\alpha,\gamma>},$$  $i\in\{1,...,M\}$ and $\gamma=(\gamma_{i})_{i\in\{1,...,M\}}$ with:
$$(43)$$

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

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

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

With this last version of the rule, for αi given by the equation (40), we obtain on our illustrative example λ = 36 13 when the experts 1, 2 and 3 say A, B, and A ∪ C respectively (the conflict is 0.21), λ =
16 5 when the conflict is 0.14 and λ =
56 17 when