
| A      | B      | A ∪ B   |        |
|--------|--------|---------|--------|
| qm1(·) | L1(NB) | L2(P S) | L3(NS) |
| qm2(·) | L4(NM) | L2(NS)  | L0(O)  |

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

Table 2: qm1(·), qm2(·**) with qualitative enriched labels**

## 6.2 Qualitative Masses With Qualitative Enriched Labels

Using qualitative supporting degrees (i.e. enriched labels of Type 2) taking their values in the linguistic set X = {NB, NM, NS, O, P S, PM, P B}, with NB ≺ NM ≺ NS ≺ O ≺ P S ≺ PM ≺ P B **we get similar result**
for this example. So, let's consider a frame Θ = {A, B} with Shafer's model and qm1(·) and qm2(·**) chosen as**
in Table 2 The qualitative conjunctive and PCR5 fusion rules are obtained with derivations identical to the previous ones, since NB ≺ NM ≺ NS ≺ O ≺ P S ≺ PM ≺ P B and we associated NB = 0.3 or less, NM = [0.5, 0.6],
NS = [0.7, 0.8], O = 1 and P S = 1.1. The minimum operator on X**(qualitative degrees) works similarly as on** R

+ **(quantitative degrees). Thus, finally one gets results according to Table 3.**

| A          | B      | A ∪ B   | A ∩ B   |        |
|------------|--------|---------|---------|--------|
| qm12(·)    | L3(NB) | L2(NS)  | L0(NS)  | L1(NB) |
| qmP CR5(·) | L4(NB) | L2(NB)  | L0(NS)  | L0(O)  |

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

Table 3: Result obtained with qualitative conjunctive and PCR5 fuion rules

## 7 Conclusion

With the recent development of qualitative methods for reasoning under uncertainty developed in Artificial Intelligence, more and more experts and scholars have great interest on qualitative information fusion, especially those working in the development of modern multi-source systems for defense, robot navigation, mapping, localization and path planning and so on. In this paper, we have proposed two possible enrichments (quantitative and/or qualitative) of linguistic labels and a simple and direct extension of the q**-operators developed in the**
DSmT framework. We have also shown how to fuse qualitative-enriched belief assignments which can be expressed in natural language by human experts. Two illustrating examples have been presented in details to explain how our qualitative-enriched operators (qe**-operators) and qualitative PCR5 rule of combination work.** Some research in robotics of the application of qe**-operators (with quantitative or qualitative supporting degrees)** is under progress and will be presented in a forthcoming publication.

## Acknowledgment

This work is partially supported by the National Nature Science Foundation of China (No.60675028).

## References

[1] S. Badaloni and M. Giacomin, "The algebra IAfuz**: a framework for qualitative fuzzy temporal reasoning,"**
Artificial Intelligence**, Vol. 170, No. 10, pp. 872–908, July 2006.**
[2] G. Brewka, S. Benferhat and D. L. Berre, "Qualitative choice logic," Artificial Intelligence**, Vol.157, No.**
1-2, pp. 203–237, August 2004.

[3] D. Dubois and H. Prade, "Representation and combination of uncertainty with belief functions and possibility measures," Computational Intelligence**, Vol. 4, pp. 244–264, 1988.**
7The confidence level/degree in the labels does not matter in the definition of quasi-normalization.