Handling imprecise evaluations in multiple criteria decision aiding and robust ordinal regression by n-point intervals
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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.
KeywordsImprecise evaluations n-point intervals Multiple criteria decision aiding Robust ordinal regression Preference relations
The first and the second authors wish to acknowledge funding by the “FIR of the University of Catania BCAEA3 New developments in Multiple Criteria Decision Aiding (MCDA) and their application to territorial competitiveness”
- Czyżak, P., & Słowiński, R. (1997). A concordance-discordance approach to multi-criteria ranking of actions with fuzzy evaluations. In J. Climaco (Ed.), Multicriteria analysis (pp. 85–93). Berlin: Springer.Google Scholar
- Hurwicz, L. (1951). A class of criteria for decision making under ignorance. Cowles series, Statistics, 356.Google Scholar
- Słowiński, R., Greco, S., & Matarazzo, B. (2009). Rough sets in decision making. In R. A. Meyers (Ed.), Encyclopedia of complexity and systems science (pp. 7753–7786). New York: Springer.Google Scholar