Skip to main content

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 68))

  • 976 Accesses

Abstract

In recent years, dealing with uncertainty using interval probabilities, such as combination, marginalization, condition, Bayesian inferences, is receiving considerable attention by researchers. However, how to elicit interval probabilities from subjective judgment is a basic problem for the applications of interval probabilities. In this paper, interval-valued pair-wise comparison of possible outcomes is considered to know which one is more likely to occur. LP-based and QP-based models proposed for estimating interval probabilities. Expectation and decision criteria under interval probabilities are given. As an application, newsvendor problem is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berleant, D., Cozman, F.G., Kosheleva, O., Kreinovich, V.: Dealing with imprecise probabilities: Interval-related talks at ISIPTA 2005. Reliable Computing 12, 153–165 (2006)

    Article  Google Scholar 

  2. Camerer, C., Weber, M.: Recent development in modeling preference: Uncertainty and ambiguity. Journal of Risk and Uncertainty 5, 325–370 (1992)

    Article  MATH  Google Scholar 

  3. Cano, A., Moral, S.: Using probability trees to compute marginals with imprecise probabilities. International Journal of Approximate Reasoning 29, 1–46 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Danielson, M., Ekenberg, L.: Computing upper and lower bounds in interval decision trees. European Journal of Operational Research 181, 808–816 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. de Finetti, B.: La prévision: Ses lois logiques, ses sources subjectives. Annales de l’Institut Henri Poincaré 7, 1–68 (1937); Translated by H. E. Kyburg as Foresight: Its logical laws, its subjective sources. In: Kyburg, H. E., Smokler, H.E. (eds.). Studies in Subjective Probability. Robert E. Krieger, New York, pp. 57–118 (1980)

    MATH  Google Scholar 

  6. de Campos, L.M., Huete, J.F., Moral, S.: Probability intervals: A tool for uncertain reasoning. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 2, 167–196 (1994)

    Article  MathSciNet  Google Scholar 

  7. Dempster, A.: Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38, 325–339 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  8. Einhorn, H.J., Hogarth, R.M.: Ambiguity and uncertainty in probabilistic inference. Psychological Review 92, 433–461 (1985)

    Article  Google Scholar 

  9. Guo, P., Tanaka, H.: Interval regression analysis and its application, ISI invited paper (IPM30: Interval and Imprecise Data Analysis). In: Proceedings of the 56th Session, Bulletin of the International Statistical Institute, Lisboa, Portugal, p. 8 (2007)

    Google Scholar 

  10. Guo, P., Tanaka, H.: Decision making with interval probabilities. European Journal of Operational Research 203, 444–454 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Khouja, M.: The single-period (news-vendor) problem: Literature review and suggestion for future research. Omega 27, 537–553 (1999)

    Article  Google Scholar 

  12. Kyburg, H.E.: Interval-valued probabilities (1999), http://www.sipta.org/documentation/

  13. Lodwick, W.A., Jamison, K.D.: Interval-valued probability in the analysis of problems containing a mixture of possibilistic, probabilistic, and interval uncertainty. Fuzzy Sets and Systems 159, 2845–2858 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Neumaier, A.: Clouds, fuzzy sets, and probability intervals. Reliable Computing 10, 249–272 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Petruzzi, N.C., Dada, M.: Pricing and the newsvendor problem: A review with extensions. Operations Research 47, 183–194 (1999)

    Article  MATH  Google Scholar 

  16. Raz, G., Porteus, E.L.: A fractiles perspective to the joint price/quantity newsvendor model. Management Science 52, 1764–1777 (2006)

    Article  Google Scholar 

  17. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  18. Silver, E.A., Pyke, D.F., Petterson, R.: Inventory Management and Production Planning and Scheduling. Wiley, New York (1998)

    Google Scholar 

  19. Smithson, M.J.: Human judgment and imprecise probabilities (1997), http://www.sipta.org/documentation/

  20. Tanaka, H., Sugihara, K., Maeda, Y.: Non-additive measure by interval probability functions. Information Sciences 164, 209–227 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Troffaes, M.C.M.: Decision making under uncertainty using imprecise probabilities. International Journal of Approximate Reasoning 45, 17–29 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  22. Walley, P.: Statistical Reasoning with Imprecise Probability. Chapman and Hall, London (1991)

    Google Scholar 

  23. Walley, P.: Inferences from multinomial data: Learning about a bag of marbles. Journal of the Royal Statistical Society B 58, 3–57 (1996)

    MATH  MathSciNet  Google Scholar 

  24. Weichselberger, K., Pohlmann, S.: A Methodology for Uncertainty in Knowledge-Based Systems. LNCS, vol. 419. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  25. Weichselberger, K.: The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning 24, 149–170 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  26. Yager, R.R., Kreinovich, V.: Decision making under interval probabilities. International Journal of Approximate Reasoning 22, 195–215 (1999)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Guo, P., Tanaka, H. (2010). On Interval Probabilities. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11960-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11959-0

  • Online ISBN: 978-3-642-11960-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics