Color distribution of three drawn balls from Ellsberg urn

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.

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

[2]  Baoding Liu.  Some Research Problems in Uncertainty Theory , 2009 .

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

[4]  Liying Liu,et al.  Stability in distribution for multifactor uncertain differential equation , 2017, J. Ambient Intell. Humaniz. Comput..

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

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

[7]  Yuhan Liu,et al.  Expected loss of uncertain random system , 2018, Soft Comput..

[8]  Yuhan Liu,et al.  Multivariate uncertain regression model with imprecise observations , 2020, J. Ambient Intell. Humaniz. Comput..

[9]  Zhongfeng Qin,et al.  Uncertain random goal programming , 2018, Fuzzy Optim. Decis. Mak..

[10]  Baoding Liu.  Why is There a Need for Uncertainty Theory , 2012 .

[11]  Hua Ke,et al.  Uncertain random multilevel programming with application to production control problem , 2015, Soft Comput..

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

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

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

[15]  Chen Xiao,et al.  Tail value-at-risk in uncertain random environment , 2018, Soft Comput..

[16]  Zhiguo Zeng,et al.  Belief reliability: a new metrics for products’ reliability , 2013, Fuzzy Optim. Decis. Mak..

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

[18]  Xin Gao,et al.  Degree-constrained minimum spanning tree problem of uncertain random network , 2017, J. Ambient Intell. Humaniz. Comput..

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

[20]  Rong Gao,et al.  Importance index of components in uncertain random systems , 2016, Knowl. Based Syst..

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

[22]  Matteo Gaeta,et al.  Fitted Q-iteration and functional networks for ubiquitous recommender systems , 2017, Soft Comput..

[23]  Xiangfeng Yang,et al.  Existence and uniqueness theorem for uncertain heat equation , 2017, J. Ambient Intell. Humaniz. Comput..