Two-degree-of-freedom Ellsberg urn problem

Traditional model assumes there is only randomness existing in the urn problem. However, if the numbers of the colored balls are unknown, then they should be regarded as uncertain variable. Since a ball is drawn randomly, Ellsberg urn problem is essentially a complicated system with randomness and uncertainty. Instead of psychological experiment, this paper applies uncertainty theory and chance theory to provide a rigorous mathematical method for formulating the general case of a one-degree-of-freedom Ellsberg urn problem. Furthermore, a two-degree-of-freedom Ellsberg urn problem is proposed, and the formulation for the problem is given to deal with three unknown numbers of colored balls.

[1]  Yuhan Liu,et al.  Value-at-risk in uncertain random risk analysis , 2017, Inf. Sci..

[2]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[3]  Rui Kang,et al.  Reliability analysis in uncertain random system , 2016, Fuzzy Optimization and Decision Making.

[4]  G. Pólya,et al.  Über die Statistik verketteter Vorgänge , 1923 .

[5]  Yuhan Liu,et al.  Uncertain random variables: a mixture of uncertainty and randomness , 2013, Soft Comput..

[6]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[7]  Yuhan Liu,et al.  Risk Index in Uncertain Random Risk Analysis , 2014, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[8]  Baoding Liu,et al.  Residual and confidence interval for uncertain regression model with imprecise observations , 2018, J. Intell. Fuzzy Syst..

[9]  Yuhan Liu,et al.  Uncertain random programming with applications , 2013, Fuzzy Optim. Decis. Mak..

[10]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[11]  Baoding Liu,et al.  Uncertain time series analysis with imprecise observations , 2018, Fuzzy Optimization and Decision Making.

[12]  Baoding Liu,et al.  Uncertain Urn Problems and Ellsberg Experiment , 2018, Soft Comput..

[13]  Kai Yao.  Uncertain Statistical Inference Models With Imprecise Observations , 2018, IEEE Transactions on Fuzzy Systems.

[14]  Yuhan Liu,et al.  Uncertain random logic and uncertain random entailment , 2017, J. Ambient Intell. Humaniz. Comput..

[15]  Jinwu Gao,et al.  Law of Large Numbers for Uncertain Random Variables , 2016, IEEE Transactions on Fuzzy Systems.

[16]  Baoding Liu,et al.  Uncertain data envelopment analysis with imprecisely observed inputs and outputs , 2018, Fuzzy Optim. Decis. Mak..

[17]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[18]  Jinwu Gao,et al.  Some Concepts and Theorems of Uncertain Random Process , 2015, Int. J. Intell. Syst..

[19]  Fan Yang,et al.  Multi-objective optimization in uncertain random environments , 2014, Fuzzy Optim. Decis. Mak..