FLARL, we can easily extend all the combination and conditioning rules from quantitative to qualitative. In the sequel we will consider s ≥ 2 qualitative belief assignments qm1(.)**, . . . , qm**s(.) defined over the same space GΘ and provided by s independent sources S1**, . . . , S**s of evidence.

Note: The addition and multiplication operators used in all qualitative fusion formulas in next sections correspond to *qualitative addition* and *qualitative multiplication* operators and must not be confused with classical addition and multiplication operators for numbers.

## 6.3 Qualitative Conjunctive Rule

The qualitative Conjunctive Rule (qCR) of s ≥ 2 sources is defined similarly to the quantitative conjunctive consensus rule, i.e.

$$qm_{qCR}(X)=\sum_{\begin{subarray}{c}X_{1},\cdots,X_{s}\in G^{\theta}\\ X_{1}\cap\cdots\cap X_{s}=X\end{subarray}}\prod_{i=1}^{s}qm_{i}(X_{i})\tag{26}$$
32
The total qualitative conflicting mass is given by

$$K_{1\ldots s}=\sum_{\begin{array}{l}{{X_{1},\ldots,X_{s}\in G^{\Theta}}}\\ {{X_{1}\cap\ldots\cap X_{s}=\emptyset}}\end{array}}\prod_{i=1}^{s}q m_{i}(X_{i})$$

## 6.4 Qualitative Dsm Classic Rule

The qualitative DSm Classic rule (q-DSmC) for s ≥ 2 is defined similarly to DSm Classic fusion rule (DSmC)
as follows : qm**qDSmC**(∅) = L0 and for all X ∈ DΘ **\ {∅}**,

$$q m_{q D S m C}(X)=\sum_{\begin{array}{l}{{X_{1},\cdots,X_{s}\in D^{\Theta}}}\\ {{X_{1}\cap\cdots\cap X_{s}=X}}\end{array}}\prod_{i=1}^{s}q m_{i}(X_{i})$$
$$(27)$$

## 6.5 Qualitative Hybrid Dsm Rule

The qualitative hybrid DSm rule (q-DSmH) is defined similarly to quantitative hybrid DSm rule [31] as follows:
qm**qDSmH**(∅) = L0 (28)

$${\mathrm{and~for~all~}}X\in G^{\Theta}\setminus\{\emptyset\}$$
$$q m_{q D S m H}(X)\triangleq\phi(X)\cdot\left[q S_{1}(X)+q S_{2}(X)+q S_{3}(X)\right]$$

where all sets involved in formulas are in the canonical form and φ(X) is the characteristic non-emptiness function of a set X, i.e. φ(X) = Lm+1 if X /∈ ∅ and φ(X) = L0 otherwise, where ∅ , {∅M, ∅}. ∅M is the set of all elements of DΘ which have been forced to be empty through the constraints of the model M and ∅ is the classical/universal empty set. qS1(X) ≡ qm**qDSmC**(X), qS2(X), qS3(X) are defined by

$$q S_{1}(X)\triangleq\sum_{\begin{array}{l}{{X_{1},X_{2},\ldots,X_{s}\in D^{\Theta}}}\\ {{X_{1}\cap X_{2}\cap\ldots\cap X_{s}=X}}\end{array}}\prod_{i=1}^{s}q m_{i}(X_{i})$$
$$(29)$$

qmi(Xi) (30)
$$q S_{2}(X)\triangleq\sum_{\begin{subarray}{c}X_{1},X_{2},\dots,X_{s}\in\Theta\\ \mathbb{I}\not=X]\vee[(\mathcal{U}\in\Theta)\wedge(X=I_{t})]\end{subarray}}\prod_{i=1}^{s}q m_{i}(X_{i})$$
$$(30)$$
$$(31)$$
