How to combine inconsistent ordinal and cardinal preferences: A satisficing modelling approach

• We deal with two conflictive sources of information about individual preferences.
• We state the problem as the search of a compromise consensus solution.
• A satisficing model based on the minimization of a distance function is proposed.

This paper analyzes a situation where a decision-maker provides cardinal and ordinal information about her/his preferences towards m objects (criteria, alternatives, etc.). However, the two rankings derived from her/his preferences are different. This situation of “inconsistent preferences” is formalized. Moreover, in order to deal with this type of conflictive situation, a satisficing model based on the minimization of p-metric distance functions is proposed. In this way, a final set of weights associated with the m objects, by using the cardinal and the ordinal information, is obtained. The final model corresponds to a linear extended goal programming, so the proposed approach is operationally and computationally efficient, since the computations are reduced to solving a small number of linear programming models of a moderate size.