

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

A represents the proposition " x ∈ [8, 15] " . N(A) = 0.75 represents the certainty level (confidence) in the proposition
"" A and Π( A ) as un upper probability for A (figure 9).

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

Any interval of the possibility distribution can be transformed into basic belief assignment (figure 10) according to relations between possibility and belief function theories  [1],
[2], [10].

![0_image_3.png](0_image_3.png)

## C. Mapping Models: A Link From Evaluation To Decision

A mapping model is a set of fuzzy intervals L - R linking a criterion evaluation and the decision classes: it plays more or less the same role than the utility function in a total aggregation based multi-criteria decision method. For each evaluation of a criterion by one source, each interval of the possibility distribution ( I ( s,int,)) is mapped to the common frame of discernment of decision according to surface ratios
(figures  11,  12). At the end of the mapping process, all the criteria evaluations provided by each source are transformed in basic belief assignments (bba's) according the common frame of discernment of decision: these bba's are then fused in a two-step process.

![0_image_2.png](0_image_2.png)

## D. Two Steps Of Fusion

After the mapping step, the ER - MCDA process is based on two successive fusion levels (figure 13). The first step consists in the fusion of bba's corresponding, for each