Skip to main content
Log in

Color distribution of three drawn balls from Ellsberg urn

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

Ellsberg urn is a complicated system with uncertainty (the unknown numbers of the colored balls) and randomness (the randomly drawn balls). By supposing that two numbers of colored balls are unknown in an Ellsberg urn, this paper applies uncertainty theory, probability theory and chance theory as rigorous mathematical tools to formulating the color distribution of the drawn balls when three balls are randomly drawn from the urn. Furthermore, an intuitive example is given to illustrate the results obtained by the mathematical method.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Eggenberger F, Pólya G (1923) Über die statistik verketteter vorgäge. Zeit Angew Math Mech 3:279–289

    Article  Google Scholar 

  • Ellsberg D (1961) Risk, ambiguity, and the savage axioms. Q J Econ 75:643–669

    Article  MathSciNet  Google Scholar 

  • Gaeta M, Orciuoli F, Rarita L, Tomasiello S (2017) Fitted Q-iteration and functional networks for ubiquitous recommender systems. Soft Comput 21(23):7067–7075

    Article  Google Scholar 

  • Gao R, Yao K (2016) Importance index of components in uncertain random systems. Knowl Based Syst 109:208–217

    Article  Google Scholar 

  • Gao X, Jia L, Kai S (2017) Degree-constrained minimum spanning tree problem of uncertain random network. J Ambient Intell Humaniz Comput 8(4):747–757

    Article  Google Scholar 

  • Ke H, Su T, Ni Y (2015) Uncertain random multilevel programming with application to product control problem. Soft Comput 19:1739–1746

    Article  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    Google Scholar 

  • Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):3–10

    Google Scholar 

  • Liu B (2019) Uncertain urn problems and Ellsberg experiment. Soft Comput 23:6579–6584

    Article  Google Scholar 

  • Liu Y (2013a) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 17:625–634

    Article  Google Scholar 

  • Liu Y (2013b) Uncertain random programming with applications. Fuzzy Optim Decis Mak 12(2):153–169

    Article  MathSciNet  Google Scholar 

  • Liu Y, Ralescu DA (2014) Risk index in uncertain random risk analysis. Int J Uncertain Fuzziness Knowl Based Syst 22(4):491–504

    Article  MathSciNet  Google Scholar 

  • Liu Y, Ralescu DA (2017) Value-at-risk in uncertain random risk analysis. Inf Sci 391–392:1–8

    MathSciNet  MATH  Google Scholar 

  • Liu Y, Ralescu DA (2018) Expected loss of uncertain random system. Soft Comput 22:5573–5578

    Article  Google Scholar 

  • Liu Y, Ralescu DA, Xiao C, Lio W (2020) Tail value-at-risk in uncertain random environment. Soft Comput 24:2495–2502

    Article  Google Scholar 

  • Ma W, Liu L, Gao R et al (2017) Stability in distribution for multifactor uncertain differential equation. J Ambient Intell Humaniz Comput 8(5):707–716

    Article  Google Scholar 

  • Qin Z (2018) Uncertain random goal programming. Fuzzy Optim Decis Mak 17:375–386

    Article  MathSciNet  Google Scholar 

  • Wen M, Kang R (2016) Reliability analysis in uncertain random system. Fuzzy Optim Decis Mak 15(4):491–506

    Article  MathSciNet  Google Scholar 

  • Zeng Z, Wen M, Kang R (2013) Belief reliability: a new metrics for products’ reliability. Fuzzy Optim Decis Mak 12(1):15–27

    Article  MathSciNet  Google Scholar 

  • Zhou J, Yang F, Wang K (2014) Multi-objective optimization in uncertain random environments. Fuzzy Optim Decis Mak 13(4):397–413

    Article  MathSciNet  Google Scholar 

  • Yang X, Ni Y (2017) Existence and uniqueness theorem for uncertain heat equation. J Ambient Intell Humaniz Comput 8(5):717–725

    Article  Google Scholar 

  • Ye T, Liu Y (2020) Multivariate uncertain regression model with imprecise observations. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-01763-z

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China Grant no. 61873329.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guangquan Cheng.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lio, W., Cheng, G. Color distribution of three drawn balls from Ellsberg urn. J Ambient Intell Human Comput 12, 3169–3176 (2021). https://doi.org/10.1007/s12652-020-02475-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-020-02475-0

Keywords

Navigation