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 (ROR) which, unlike other MCDA methods, takes into account all compatible instances of an adopted preference model, which reproduce an indirect preference information ⋆ [Post-print] Please cite as: Corrente Salvatore, Greco Salvatore, S lowiński Roman. Handling Imprecise Evaluations in Multiple Criteria Decision Aiding and Robust Ordinal Regression by n-point intervals. Fuzzy Optimization and Decision Making. DOI: 10.1007/s10700-016-9244-x S. Corrente · S. Greco Department of Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy E-mail: [email protected] S. Greco University of Portsmouth, Portsmouth Business School, Centre of Operations Research and Logistics (CORL), Richmond Building, Portland Street, Portsmouth PO1 3DE, United Kingdom E-mail: [email protected] R. S lowiński Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, and Systems Research Institute, Polish Academy of Sciences, 01-447 Warsaw, Poland E-mail: [email protected] n-point intervals in MCDA and ROR 1 provided by the Decision Maker (DM). An illustrative example shows how the method can be applied in practice.