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Fuzzy Optimization and Decision Making

, Volume 16, Issue 2, pp 127–157 | Cite as

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

  • Salvatore CorrenteEmail author
  • Salvatore Greco
  • Roman Słowiński
Article

Abstract

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.

Keywords

Imprecise evaluations n-point intervals Multiple criteria decision aiding Robust ordinal regression Preference relations 

Notes

Acknowledgments

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”

References

  1. Corrente, S., Greco, S., & Słowiński, R. (2012). Multiple criteria hierarchy process in robust ordinal regression. Decision Support Systems, 53(3), 660–674.CrossRefGoogle Scholar
  2. Corrente, S., Greco, S., Kadziński, M., & Słowiński, R. (2013). Robust ordinal regression in preference learning and ranking. Machine Learning, 93, 381–422.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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
  4. Dembczynski, K., Greco, S., & Słowiński, R. (2009). Rough set approach to multiple criteria classification with imprecise evaluations and assignments. European Journal of Operational Research, 198(2), 626–636.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Dong, Y., & Herrera-Viedma, E. (2015). Consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relation. Cybernetics, IEEE Transactions on, 45(4), 780–792.CrossRefGoogle Scholar
  6. Dubois, D. (2011). The role of fuzzy sets in decision sciences: Old techniques and new directions. Fuzzy Sets and Systems, 184(1), 3–28.MathSciNetCrossRefzbMATHGoogle Scholar
  7. Figueira, J., Greco, S., & Ehrgott, M. (2005). Multiple criteria decision analysis: State of the art surveys. Berlin: Springer.CrossRefzbMATHGoogle Scholar
  8. Fishburn, P. C. (1985). Interval orders and interval graphs. New York: Wiley.zbMATHGoogle Scholar
  9. Giarlotta, A., & Greco, S. (2013). Necessary and possible preference structures. Journal of Mathematical Economics, 49(2), 163–172.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Greco, S., Matarazzo, B., & Słowiński, R. (2001). Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129(1), 1–47.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Greco, S., Mousseau, V., & Słowiński, R. (2008). Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions. European Journal of Operational Research, 191(2), 416–436.MathSciNetCrossRefzbMATHGoogle Scholar
  12. Herrera, F., Alonso, S., Chiclana, F., & Herrera-Viedma, E. (2009). Computing with words in decision making: Foundations, trends and prospects. Fuzzy Optimization and Decision Making, 8(4), 337–364.CrossRefzbMATHGoogle Scholar
  13. Hurwicz, L. (1951). A class of criteria for decision making under ignorance. Cowles series, Statistics, 356.Google Scholar
  14. Jacquet-Lagreze, E., & Siskos, J. (2001). Preference disaggregation: 20 years of MCDA experience. European Journal of Operational Research, 130(2), 233–245.CrossRefzbMATHGoogle Scholar
  15. Keeney, R. L., & Raiffa, H. (1993). Decisions with multiple objectives: Preferences and value tradeoffs. New York: Wiley.CrossRefzbMATHGoogle Scholar
  16. Lahdelma, R., Hokkanen, J., & Salminen, P. (1998). SMAA-stochastic multiobjective acceptability analysis. European Journal of Operational Research, 106(1), 137–143.CrossRefGoogle Scholar
  17. Moskowitz, H., Preckel, P. V., & Yang, A. (1993). Decision analysis with incomplete utility and probability information. Operations Research, 106(1), 137–143.zbMATHGoogle Scholar
  18. Ozturk, M., Pirlot, M., & Tsoukias, A. (2011). Representing preferences using intervals. Artificial Intelligence, 175(7–8), 1194–1222.MathSciNetCrossRefzbMATHGoogle Scholar
  19. Park, K. S., & Kim, S. J. (1997). Tools for interactive multiattribute decision-making with incompletely identified information. European Journal of Operational Research, 98(1), 111–123.CrossRefzbMATHGoogle Scholar
  20. Roy, B. (1993). Decision science or decision-aid science? European Journal of Operational Research, 66(2), 184–203.CrossRefGoogle Scholar
  21. Roy, B. (1996). Multicriteria methodology for decision aiding. Dordrecht: Kluwer.CrossRefzbMATHGoogle Scholar
  22. Roy, B., & Słowiński, R. (2013). Questions guiding the choice of a multicriteria decision aiding method. EURO Journal on Decision Processes, 1(1), 69–97.CrossRefGoogle Scholar
  23. 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
  24. Weber, M. (1987). Decision making with incomplete information. European Journal of Operational Research, 28(1), 44–57.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Zadeh, L. H. (1975). The concept of a linguistic variable and its application to approximate reasoning. Information Science, 1(8), 199–249.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Salvatore Corrente
    • 1
    Email author
  • Salvatore Greco
    • 1
    • 2
  • Roman Słowiński
    • 3
    • 4
  1. 1.Department of Economics and BusinessUniversity of CataniaCataniaItaly
  2. 2.Portsmouth Business School Centre of Operations Research and Logistics (CORL)University of PortsmouthPortsmouthUK
  3. 3.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  4. 4.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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