Handling imprecise evaluations in multiple criteria decision aiding and robust ordinal regression by n-point intervals

We consider imprecise evaluation of alternatives in multiple criteria ranking problems. The imprecise evaluations are represented by n-point intervals which are defined by the largest interval of possible evaluations and by its subintervals sequentially nested one in another. This sequence of subintervals is associated with an increasing sequence of plausibility, such that the plausibility of a subinterval is greater than the plausibility of the subinterval containing it. We explain the intuition that stands behind this proposal, and we show the advantage of n-point intervals compared to other methods dealing with imprecise evaluations. Although n-point intervals can be applied in any multiple criteria decision aiding (MCDA) method, in this paper, we focus on their application in robust ordinal regression which, unlike other MCDA methods, takes into account all compatible instances of an adopted preference model, which reproduce an indirect preference information provided by the decision maker. An illustrative example shows how the method can be applied in practice.