Dealing with inconsistent judgments in multiple criteria sorting models

Some decision problems can be formulated as sorting models which consist in assigning alternatives evaluated on several criteria to ordered categories. The implementation of a multiple criteria sorting model requires to set the values of the preference parameters used in the model. Rather than ¯xing directly the values of these parameters, an usual approach is to infer these values from assignment examples provided by the decision maker (DM), i.e., alternatives for which he/she speci¯es a required category or interval of acceptable categories. However, the judgments expressed by DMs through assignment examples can be inconsis- tent, i.e., may not match the sorting model. In such situations, it is necessary to support the DMs in the resolution of this inconsistency. In this paper, we propose algorithms that calculate di®erent ways to modify the set of assignment examples so that the information can be represented in the sorting model. The modi¯cations considered are either the removal of examples or the relaxation of existing assignments. These algorithms incorpo- rate information about the con¯dence attached by the DMs to each assignment example. These algorithms aim at ¯nding and ranking the solutions to solve inconsistency that the DMs are most likely to accept