Subadditivity of chance measure

Chance theory is a mathematical methodology for dealing with indeterminacy phenomena involving uncertainty and randomness. In this paper, some properties of chance space are investigated. Based on this, the subadditivity theorem, null-additivity theorem, and asymptotic theorem of chance measure are proved.

[1]  Yuhong Sheng,et al.  Stability in p-th moment for uncertain differential equation , 2014, J. Intell. Fuzzy Syst..

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

[3]  Samarjit Kar,et al.  Cross-entropy measure of uncertain variables , 2012, Inf. Sci..

[4]  Kakuzo Iwamura,et al.  A sufficient and necessary condition of uncertainty distribution , 2010 .

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

[6]  Baoding Liu Toward uncertain finance theory , 2013 .

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

[8]  Yuhan Liu,et al.  Expected Value of Function of Uncertain Variables , 2010 .

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

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

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

[12]  D. Ralescu,et al.  Liu process and uncertain calculus , 2013 .

[13]  A. Kolmogoroff Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

[14]  Wei Dai,et al.  Entropy of function of uncertain variables , 2012, Math. Comput. Model..

[15]  Baoding Liu Uncertain Random Graph and Uncertain Random Network Baoding , 2014 .

[16]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

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

[18]  Xiaowei Chen,et al.  Maximum Entropy Principle for Uncertain Variables , 2011 .

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

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