Distance between Uncertain Random Variables

Distance between Uncertain Random Variables

Yongchao Hou Weicai Peng 

Department of Mathematical Sciences, Chaohu University, Anhui 238000, China

Corresponding Author Email: 
hyc@chu.edu.cn, weicaipeng@126.com
30 September 2014
| Citation



In order to deal with indeterminacy data involving uncertainty and randomness, uncertain random variable is investigated by many scholars. As an extension of distance between uncertain variables, the definition of distance between uncertain random variables is proposed in this paper. Then, some formulas are provided to calculate distances between particular types of uncertain random variables


uncertainty theory; uncertain random variable; chance measure; distance. 

1. Introduction
2. Preliminary
3. Distance between Uncertain Random Variables
4. Conclusions

This work was supported by the National Natural Science Foundation of China Grant (No.61273044) and the Foundation of Anhui Educational Committee (No. KJ2014A174, No. KJ2011B105).


[1] Chen X. and Dai W., Maximum entropy principle for uncertain variables. International Journal of Fuzzy Systems, vol.13, No.3, pp.232-236, 2011. 

[2] Chen X., Kar S., and Ralescu D., Cross-entropy measure of uncertain variables. Information Sciences, Vol.201, pp.53-60, 2012. 

[3] Dai W. and Chen X., Entropy of function of uncertain variables. Mathematical and Computer Modelling, vol.55, Nos.3-4, pp.754-760, 2012. 

[4] Hou Y., Subadditivity of chance measure. Journal of Uncertainty Analysis and Applications, vol.2:14, 2014. 

[5] Kolmogorov AN, Grundbegriffe der wahrscheinlich-keitsrechnung, Julius Springer, Berlin, 1933. 

[6] Li X. and Liu B., On distance between fuzzy variables. Journal of Intelligent and Fuzzy Systems, vol.19, No.3, pp.197-204, 2008. 

[7] Liu B., Uncertainty Theory, 2nd Edition, Springer-Verlag, Berlin, 2007. 

[8] Liu B., Theory and Practice of Uncertain Programming, 2nd Edition, Springer-Verlag, Berlin, 2009. 

[9] Liu B., Some research problems in uncertainty theory. Journal of Uncertain Systems, vol.3(1), pp.3-10, 2009. 

[10] Liu B., Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, 2010. 

[11] Liu B., Why is there a need for uncertainty theory. Journal of Uncertain Systems, vol.6, No.1, pp. 3-10, 2012. 

[12] Liu B., Uncertain random graphs and uncertain random networks, Technical Report, 2013. 

[13] Liu Y. and Ha M., Expected value of function of uncertain variables. Journal of Uncertain Systems, vol.4, No.3, pp.181-186, 2010. 

[14] Liu Y., Uncertain random variables: A mixture of uncertainty and randomness. Soft Computing, vol.17, No.4, pp.625-634, 2013. 

[15] Liu Y., Uncertain random programming with applications. Fuzzy Optimization and Decision Making, vol.12, No.2, pp.153-169, 2013. 

[16] Liu Y., Risk index in uncertain random risk analysis, http://orsc.edu.cn/online/130403.pdf. 

[17] Liu Y., Uncertain random logic and uncertain random entailment, Technical Report, 2013. 

[18] Peng Z. and Iwamura K., A sufficient and necessary condition of uncertainty distribution. Journal of Interdisciplinary Mathematics, vol.13, No.3, pp.277-285, 2010. 

[19] Sheng Y., Stability in the p-th moment for uncertain differential equation, Journal of Intelligent and Fuzzy Systems, to be published, http://orsc.edu.cn/online/1211-20.pdf. 

[20] Wen M. and Kang R., Reliability analysis in uncertain random system, http://orsc.edu.cn/online/120419.pdf. 

[21] Yang L. and Liu B., On continuity theorem for characteristic function of fuzzy variable. Journal of Intelligent and Fuzzy Systems, vol.17, No.3, pp. 325-332, 2006. 

[22] Yao K. and Gao J, Law of large numbers for uncertain random variables, http://orsc.edu.cn/on-line/120401.pdf. 

[23] Yao K. and Gao J, Some concepts and theorems of uncertain random process, http://orsc.edu.cn/on-line/120402.pdf. 

[24] Yao K. and Chen X., A numerical method for solving uncertain differential equations, Journal of Intelligent and Fuzzy Systems, to be published, http://orsc.edu.cn/online/110913.pdf. 

[25] Zhu Y. and Ji X., Expected values of functions of fuzzy variables. Journal of Intelligent and Fuzzy Systems, vol.17, No.5, pp.471-478, 2006.