Decision Making Under Interval Uncertainty (and Beyond)

  • Vladik Kreinovich
Part of the Studies in Computational Intelligence book series (SCI, volume 502)


To make a decision, we must find out the user’s preference, and help the user select an alternative which is the best—according to these preferences. Traditional utility-based decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is often unable to select one of these alternatives. In this chapter, we show how we can extend the utility-based decision theory to such realistic (interval) cases.


Decision Making Interval Uncertainty Utility 



This work was supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, by Grant 1 T36 GM078000-01 from the National Institutes of Health, and by a grant on F-transforms from the Office of Naval Research. The authors is greatly thankful to the anonymous referees for valuable suggestions.


  1. 1.
    Aliev, R., Huseynov, O., Kreinovich, V.: Decision making under interval and fuzzy uncertainty: towards an operational approach. In: Proceedings of the Tenth International Conference on Application of Fuzzy Systems and Soft Computing ICAFS’2012, Lisbon, Portugal, 29–30 August 2012Google Scholar
  2. 2.
    Aubinet, M., Vesala, T., Papale, D. (eds.): Eddy Covariance - A Practical Guide to Measurement and Data Analysis. Springer, Dordrecht (2012)Google Scholar
  3. 3.
    Binder, A.B., Roberts, D. L.: Criteria for Lunar Site Selection, Report No. P-30, NASA Appollo Lunar Exploration Office and Illinois Institute of Technology Research Institute, Chicago, Illinois, January 1970Google Scholar
  4. 4.
    Cobb, C.W., Douglas, P.H.: A theory of production. Am. Econ. Rev. 18(Supplement), 139–165 (1928)Google Scholar
  5. 5.
    de Finetti, B.: Theory of Probability, Wiley, New York, Vol. 1, 1974; Vol. 2, 1975Google Scholar
  6. 6.
    Ehrgott, M., Gandibleux, X. (eds.): Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Springer, New York (2002)Google Scholar
  7. 7.
    Ferson, S., Kreinovich, V., Hajagos, J., Oberkampf, W., Ginzburg, L.: Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty, Sandia National Laboratories (2007), Publ. 2007–0939Google Scholar
  8. 8.
    Fishburn, P.C.: Utility Theory for Decision Making. Wiley, New York (1969)Google Scholar
  9. 9.
    Fishburn, P.C.: Nonlinear Preference and Utility Theory. Johns Hopkins University Press, Baltimore (1988)MATHGoogle Scholar
  10. 10.
    Fountoulis, I., Mariokalos, D., Spyridonos, E., Andreakis, E.: Geological criteria and methodology for landfill sites selection. In: Proceedings of the 8th International Conference on Environmental Science and Technology, Greece, 8–10 September 2003, pp. 200–207Google Scholar
  11. 11.
    Gardeñes, E., et al.: Modal intervals. Reliable Comput. 7, 77–111 (2001)CrossRefMATHGoogle Scholar
  12. 12.
    Giang, P.H.: Decision with dempster-shafer belief functions: decision under ignorance and sequential consistency. Int. J. Approximate Reasoning 53, 38–53 (2012)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Guo, P., Tanaka, H.: Decision making with interval probabilities. Eur. J. Oper. Res. 203, 444–454 (2010)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Guo, P., Wang, Y.: Eliciting dual interval probabilities from interval comparison matrices. Inf. Sci. 190, 17–26 (2012)CrossRefMATHGoogle Scholar
  15. 15.
    Helversen B.V., Mata R.: Losing a dime with a satisfied mind: positive affect predicts less search in sequential decision making, Psychology and Aging, 27, 825–839 (2012)Google Scholar
  16. 16.
    Hurwicz, L.: Optimality Criteria for Decision Making Under Ignorance, Cowles Commission Discussion Paper, Statistics, No. 370, 1951Google Scholar
  17. 17.
    Jaimes A., Salayandia L., Gallegos I.: New cyber infrastructure for studying land-atmosphere interactions using eddy covariance techniques. In: Abstracts of the 2010 Fall Meeting American Geophysical Union AGU’2010, San Francisco, California, 12–18 December 2010Google Scholar
  18. 18.
    Jaimes, A., Herrera, J., GonzÍez, L., Ramìrez, G., Laney, C., Browning, D., Peters, D., Litvak, M., Tweedie, C.: Towards a multiscale approach to link climate, NEE and optical properties from a flux tower, robotic tram system that measures hyperspectral reflectance, phenocams, phenostations and a sensor network in desert a shrubland. In: Proceedings of the FLUXNET and Remote Sensing Open Workshop: Towards Upscaling Flux Information from Towers to the Globe FLUXNET-SpecNet’2011, Berkeley, California, 7–9 June 2011Google Scholar
  19. 19.
    Jaimes, A.: A cyber-Tool to Optimize Site Selection for Establishing an Eddy Covraince and Robotic Tram System at the Jornada Experimental Range. University of Texas, El Paso (2008)Google Scholar
  20. 20.
    Jaimes, A., Tweedie, C., Kreinovich, V., Ceberio, M.: Scale-invariant approach to multi-criterion optimization under uncertainty, with applications to optimal sensor placement, in particular, to sensor placement in environmental research. Int. J. Reliab. Saf. 6(1–3), 188–203 (2012)Google Scholar
  21. 21.
    Kiekintveld, C., Kreinovich, V.: Efficient approximation for security games with interval uncertainty, In: Proceedings of the AAAI Spring Symposium on Game Theory for Security, Sustainability, and Health GTSSH’2012, Stanford, 26–28 March 2012Google Scholar
  22. 22.
    Kintisch, E.: Loss of carbon observatory highlights gaps in data. Science 323, 1276–1277 (2009)CrossRefGoogle Scholar
  23. 23.
    Kreinovich, V.: Decision making under interval uncertainty, In: Abstracts of the 15th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computation SCAN’2012. Novosibirsk, Russia, September 2012Google Scholar
  24. 24.
    Kreinovich, V., Starks, S.A., Iourinski, D., Kosheleva, O., Finkelstein, A.: Open-ended configurations of radio telescopes: a geometrical analysis. Geombinatorics 13(2), 79–85 (2003)MathSciNetMATHGoogle Scholar
  25. 25.
    Kyburg, H.E., Smokler, H.E. (eds.): Studies in Subjective Probability. Wiley, New York (1964)Google Scholar
  26. 26.
    Luce R.D., Krantz D.H., Suppes P., Tversky A.: Foundations of measurement, vol. 3, Representation, Axiomatization, and Invariance, Academic Press, California (1990)Google Scholar
  27. 27.
    Luce, R.D., Raiffa, R.: Games and Decisions: Introduction and Critical Survey. Dover, New York (1989)MATHGoogle Scholar
  28. 28.
    Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Pennsylvania (2009)CrossRefMATHGoogle Scholar
  29. 29.
    Myerson, R.B.: Game theory. Analysis of conflict, Harvard University Press, Cambridge (1991)Google Scholar
  30. 30.
    Nash, J.F.: The bargaining problem. Econometrica 28, 155–162 (1950)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Nash, J.: Two-person cooperative games. Econometrica 21, 128–140 (1953)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Nguyen, H.T., Kreinovich, V., Wu, B., Xiang G.: Computing Statistics under Interval and Fuzzy Uncertainty, Springer, Berlin (2012)Google Scholar
  33. 33.
    Nguyen, H.T., Kreinovich, V.: Applications of Continuous Mathematics to Computer Science. Kluwer, Dordrecht (1997)MATHGoogle Scholar
  34. 34.
    Pfanzangl, J.: Theory of Measurement. Wiley, New York (1968)Google Scholar
  35. 35.
    Raiffa, H.: Decision Analysis. McGraw-Hill, Columbus (1997)Google Scholar
  36. 36.
    Roth, A.: Axiomatic Models of Bargaining. Springer, Berlin (1979)CrossRefMATHGoogle Scholar
  37. 37.
    Savage, L.J.: The Foundations of Statistics. Wiley, New York (1954)MATHGoogle Scholar
  38. 38.
    Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization. Academic Press, Orlando (1985)MATHGoogle Scholar
  39. 39.
    Shary, S.P.: A new technique in systems analysis under interval uncertainty and ambiguity. Reliable Comput. 8, 321–418 (2002)MathSciNetCrossRefMATHGoogle Scholar
  40. 40.
    Steuer, R.E.: Multiple Criteria Optimization: Theory, Computations, and Application. Wiley, New York (1986)Google Scholar
  41. 41.
    Stevens, S.S.: On the theory of scales of measurement. Science 103, 677–680 (1946)CrossRefMATHGoogle Scholar
  42. 42.
    Troffaes, M.C.M.: Decision making under uncertainty using imprecise probabilities. Int. J. Approximate Reasoning 45, 7–29 (2007)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Walsh, C.: Monetary Theory and Policy. MIT Press, Cambridge (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

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