A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

In this paper we propose a new distance measure between two preorders where the indifference, strict preference, weak preference and incomparability relations are considered. This distance measure is then used in the aggregation stage of a multiple criteria aggregation procedure for mixed evaluations designed to deal with different kinds of information imperfections. Introducing the weak preference relation allows for more nuance and flexibility to the decision-maker in this context.