Skip to main content

An Extension of Stochastic Dominance to Fuzzy Random Variables

  • Conference paper
Computational Intelligence for Knowledge-Based Systems Design (IPMU 2010)

Abstract

This paper proposes a joint extension of interval comparison and random variable comparison methods to the ranking of fuzzy random variables. First, an extension of stochastic dominance to random intervals is proposed. It enables to retrieve some previous ranking methods for belief functions and for fuzzy intervals. On this basis, a direct extension of stochastic dominance to fuzzy random variables is proposed. This approach is just one among various possibilities obtained by combining fuzzy interval and random variable comparison methods.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Chanas, S., Delgado, M., Verdegay, J.L., Vila, M.A.: Ranking fuzzy real intervals in the setting of random sets. Information Sciences 69, 201–217 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chanas, S., Zielinski, P.: Ranking fuzzy real intervals in the setting of random sets-further results. Information Sciences 117, 191–200 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chateauneuf, A., Cohen, M., Tallon, J.-M.: Decision under Risk: The Classical Expected Utility Model. In: Bouyssou, D., Dubois, D., Pirlot, M., Prade, H. (eds.) Decision-Making Process, ch. 8, pp. 363–382. ISTE, London (2009)

    Google Scholar 

  4. Couso, I., Dubois, D.: On the variability of the concept of variance for fuzzy random variables. I.E.E.E. Trans. on Fuzzy Systems 17, 1070–1080 (2009)

    Article  Google Scholar 

  5. De Baets, B., De Meyer, H.: On the cycle-transitive comparison of artificially coupled random variables. Int. J. Approximate Reasoning 47, 306–322 (2008)

    Article  MATH  Google Scholar 

  6. Denoeux, T.: Extending stochastic order to belief functions on the real line. Information Sciences 179, 1362–1376 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dubois, D.: Linear programming with fuzzy data. In: Bezdek, J.C. (ed.) Analysis of Fuzzy Information, vol. III, pp. 241–263. CRC Press, Boca Raton (1987)

    Google Scholar 

  8. Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. of Systems Science 30, 613–626 (1978)

    Article  MathSciNet  Google Scholar 

  9. Dubois, D., Prade, H.: Ranking fuzzy numbers in the setting of possibility theory. Information Sciences 30, 183–224 (2003)

    Article  MathSciNet  Google Scholar 

  10. Dubois, D., Prade, H.: Random sets and fuzzy interval analysis. Fuzzy Sets and Systems 42, 87–101 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fishburn, P.: Interval Orderings. Wiley, New-York (1987)

    Google Scholar 

  12. Kruse, R., Meyer, K.D.: Statistics with Vague Data. D. Reidel Publishing Company, Dordrecht (1987)

    MATH  Google Scholar 

  13. Kwakernaak, H.: Fuzzy random variables, I. Definitions and theorems, Information Sciences 15, 1–29 (1978)

    MATH  MathSciNet  Google Scholar 

  14. Mosler, K., Scarsini, M.: Stochastic Orders and Decision under Risk. IMS Lecture Notes, pp. 261–284 (1991)

    Google Scholar 

  15. Puri, M.L., Ralescu, D.: Fuzzy random variables. J. Math. Anal. and Appl. 114, 409–420 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  16. Smets, P.: Belief functions on real numbers. Int. J. of Approximate Reasoning 40, 181–223 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Wang, X., Kerre, E.: Reasonable properties for the ordering of fuzzy quantities (2 parts). Fuzzy Sets and Systems 118, 375–406 (2001)

    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 paper

Cite this paper

Aiche, F., Dubois, D. (2010). An Extension of Stochastic Dominance to Fuzzy Random Variables. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14049-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14048-8

  • Online ISBN: 978-3-642-14049-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics