$$(25)$$
18
$L_{\frac{285}{84}}+L_{\frac{104}{84}}+L_{\frac{28}{84}}=L_{\frac{504}{84}}=L_6=L_{\max}$. 
However, if we approximate, it is not quasi-normalized any longer since:

$$L_{[\frac{285}{84}]}+L_{[\frac{121}{84}]}+L_{[\frac{28}{84}]}=L_{3}+L_{2}+L_{0}=L_{5}\neq L_{6}=L_{\mathrm{max}}.$$

In general, if we do not approximate, and we work with quasi-normalized qualitative masses, no matter what fusion rule we apply, the result will be quasi-normalized. If we approximate, many times the quasi-normalization is lost.

## V. Generalization Of Quantitative Fusion Rules

In [1], [29] we can find two propositions of a general formulation of the combination rules. In the first one, Smets considers the combination rules from a matrix notation and find the shape of this matrix according to some assumptions on the rule, such as linearity, commutativity, associativity, etc. In the second one, a generic operator is defined from the plausibility functions.

A general formulation of the global conflict repartition have been proposed in [8], [12] for all X ∈ 2 Θ by:

$$m_{c}(X)=m_{\wedge}(X)+w(X)m_{\wedge}(\varnothing),$$
mc(X) = m∧(X) + w(X)m∧(∅), (25)
where $\sum_{X\in2\Theta}w(X)=1$. The prob 
w(X**) = 1**. The problem is the choice of the weights w(X).
A. How to choose conjunctive and disjunctive rules?

We have seen that conjunctive rule reduces the imprecision and uncertainty but can be used only if one of the experts is reliable, whereas the disjunctive rule can be used when the experts are not reliable, but allows a loss of specificity.

Hence, Florea [7] proposes a weighted sum of these two rules according to the global conflict k = m∧(∅) given for X ∈ 2 Θ
by:

$$m_{\mathrm{Flo}}(X)=\beta_{1}(k)m_{\vee}(X)+\beta_{2}(k)m_{\wedge}(X),$$
where $\beta_{1}$ and $\beta_{2}$ can admit $k=\frac{1}{2}$
2
: $ k=\frac{1}{2}$ as symmetric weight:
$$(26)$$

$$\beta_{1}(k)=\frac{k}{1-k+k^{2}},$$ $$\beta_{2}(k)=\frac{1-k}{1-k+k^{2}}.\tag{1}$$
$$(27)$$

Consequently, if the global conflict is high (k near 1) the behavior of this rule will give more importance to the disjunctive rule. Thus, this rule considers the global conflict coming from the non-reliability of the experts.

In order to take into account the weights more precisely in each partial combination, we propose the following new rule.

For two basic belief assignments m1 and m2 and for all X ∈ GΘ, X 6= ∅ we have:

mMix(X) = X Y1∪Y2=X δ1(Y1, Y2)m1(Y1)m2(Y2) + X Y1∩Y2=X δ2(Y1, Y2)m1(Y1)m2(Y2). (28) Of course, if δ1(Y1, Y2) = β1(k) and δ2(Y1, Y2) = β2(k) we obtain Florea's rule. In the same manner, if δ1(Y1, Y2) = 1 − δ2(Y1, Y2) = 0 we obtain the conjunctive rule and if δ1(Y1, Y2) = 1 − δ2(Y1, Y2) = 1 the disjunctive rule. If δ1(Y1, Y2) =