with the same notations that in the equation (18), and f **an increasing function**
defined by the mapping of [0, **1] onto IR**+.

The second generalized rule is given by:

mPCR6g(X) = mc(X) +X M i=1 X M−1 ∩ k=1 Yσi (k)∩X≡∅ (Yσi (1),...,Yσi (M−1))∈(DΘ)M−1 (20) mi(X)  MY−1 j=1 mσi(j)(Yσi(j)) ! Y Yσi (j)=X 1lj>i!g   mi(X)+X Yσi (j)=X mσi(j)(Yσi(j)) ! X g  X mσi(j)(Yσi(j)) + mi(X)1lX=Z  ,

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

with the same notations that in the equation (18), and g **an increasing function**
defined by the mapping of [0, **1] onto IR**+.

For instance, we can choose f(x) = g(x) = x α**, with** α ∈ IR+.

Algorithms for the Dubois and Prade (equation (6)), the PCR5 (equation
(15)), the PCR6 (equation (18)), the PCR6f (equation (19)), and the PCR6g (equation (20)) combinations are given in appendix.

## Remarks On The Generalized Pcr Rules

•
$\bigcap\limits_{k=1}^{M-1}Y_{k}\cap X\equiv\emptyset$ means that $\bigcap\limits_{k=1}^{M-1}Y_{k}\cap X$ is considered as a conflict by the model: $m_{i}(X)\prod\limits_{k=1}^{M-1}m_{\sigma_{i}(k)}(Y_{\sigma_{i}(k)})$ has to be redistributed on $X$ and the $Y_{k}$. 
$$Y_{k}.$$
- **The second term of the equation (18) is null if**
M−1
∩
k=1 Yk ∩ X 6≡ ∅**, hence in**
a general model in DΘ for all X and Y ∈ DΘ, X ∩ Y 6= ∅**. The PCR5**
and PCR6 are exactly the conjunctive rule: there is never any conflict.

However in 22 Θ, ∃**X, Y** ∈ 2 2 Θ**such as** X ∩ Y = ∅.

- **One of the principal problem of the PCR5 and PCR6 rules is the non**
associativity. That is is a real problem for dynamic fusion. Take for example three experts and two classes giving:

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

If we fuse the expert 1 and 2 and then 3, the PCR5 and the PCR6 rules give:
m12(A) = 0.5, m12(B**) = 0**.5,