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Uncertainty and imprecision in multi-criteria decision models has been early considered [23]. **MAUT** in general [28]
and AHP in particular have already been associated to the Evidence Theory [3], [4] including the cases of several sources [5]. A methodology called ER−**MCDA** (Evidential Reasoning - Multi-Criteria Decision Analysis) mixing multicriteria decision analysis and information fusion [25], [26]
is proposed to help the experts in a context of imperfect information. Its main principles are described in section III.

## Iii. The Er − **Mcda** Methodology

The principle of the ER − **MCDA** methodology is to use the multi-criteria decision analysis framework to analyze the decision problem and to identify the criteria involved in decision. Utility functions and aggregation steps are respectively replaced by successive mapping and fusion processes.

The main steps of this methodology consist in (figure 6)
(1) analyzing the decision problem through a hierarchical structure, (2) defining the evaluation classes for decision through a common frame of discernment, (3) evaluating the qualitative or quantitative criteria, (4) mapping the evaluations of criteria into the common frame of discernment for decision, (5) fusing the mapped evaluations of criteria to get a basic belief assignment related to the evaluations classes of decision (frame of discernment for decision). These steps are independent one from each other. Therefore, imprecise and uncertain evaluations of quantitative or qualitative criteria can be done by the sources (experts) and re-used with different mapping models.

## A. Decision Problem Elicitation

The methodology is described through a sample problem dealing with the sensitivity of an avalanche prone area (figure 7) derived from a real existing decision framework used to identify the sensitive avalanche paths [18]. For each avalanche path, decision consists in choosing between sensitivity levels described as not, low, medium or high sensitive paths. This sensitivity depends on both vulnerability and hazard levels.

Vulnerability is assessed through the number of winter permanent occupants (quantitative criterion) and existing infrastructures (qualitative criterion).

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Sensitivity levels are the elements of the common frame of discernment for decision. The fusion process will provide basic belief assignments on each or combination of the elements of this frame of discernment. In the classical DST
framework based on exhaustive and exclusive hypotheses, the frame Θ is composed of 4 exclusive elements defined by HD1 = 'No sensitivity', HD2 = 'Low sensitivity', HD3 = 'Medium sensitivity' and HD4 = 'High sensitivity'.

In the **DSmT** framework (allowing non-empty intersections),
the frame Θ is composed of 3 elements defined by HD1 = 'No sensitivity', HD2 = 'Low sensitivity' and HD3 = 'High sensitivity' (figure 8).

## B. Evaluation Of Quantitative Criteria

The quantitative criterion are evaluated through possibility distributions which allow to represent both imprecision and uncertainty. The source (an expert) provides evaluations as intervals. Let us take as an example the criterion C111 corresponding to the number of permanent winter occupants: