Some formulas of variance of uncertain random variable
Tóm tắt
Uncertainty and randomness are two basic types of indeterminacy. Chance theory was founded for modeling complex systems with not only uncertainty but also randomness. As a mixture of randomness and uncertainty, an uncertain random variable is a measurable function on the chance space. It is usually used to deal with measurable functions of uncertain variables and random variables. There are some important characteristics about uncertain random variables. The expected value is the average value of uncertain random variable in the sense of chance measure and represents the size of uncertain random variable. The variance of uncertain random variable provides a degree of the spread of the distribution around its expected value. In order to describe the variance of uncertain random variable, this paper provides some formulas to calculate the variance of uncertain random variables through chance distribution and inverse chance distribution. Several practical examples are also provided to calculate the variance for through chance distribution inverse chance distribution.
Tài liệu tham khảo
Kolmogorov AN: Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Julius Springer; 1933.
Kahneman D, Tversky A: Prospect theory: an analysis of decision under risk. Econometrica 1979, 47(2):263—292.
Liu B: Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Berlin: Springer-Verlag; 2010.
Liu B: Why is there a need for uncertainty theory? J. Uncertain Syst 2012, 6(1):3–10.
Liu B: Uncertainty Theory. Berlin: Springer-Verlag; 2007.
Liu B: Some research problems in uncertainty theory. J. Uncertain Syst 2009, 3(1):3–10.
Gao X: Some properties of continuous uncertain measure. Int. J. Uncertainty Fuzziness Knowledge-Based Syst 2009, 17(3):419–426. 10.1142/S0218488509005954
Peng ZX, Iwamura K: A sufficient and necessary condition of uncertainty distribution. J. Interdiscip. Math 2010, 13(3):277–285. 10.1080/09720502.2010.10700701
Liu YH, Ha MH: Expected value of function of uncertain variables. J. Uncertain Syst 2010, 4(3):181—186.
Yao K: A formula to calculate the variance of uncertain variable. . http://orsc.edu.cn/online/130831.pdf
Sheng YH, Samarjit K: Some results of moments of uncertain variable through inverse uncertainty distribution. Fuzzy Optimization Decis. Making (2014 in press)
Liu YH: Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 2013, 17(4):625–634. 10.1007/s00500-012-0935-0
Liu YH: Uncertain random programming with applications. Fuzzy Optimization Decis. Making 2013, 12(2):153—169.
Guo HY, Wang XS: Variance of uncertain random variables. J. Uncertainty Anal. Appl (2014 in press)
Yao K, Gao JW: Law of large numbers for uncertain random variables. . http://www.orsc.edu.cn-/online/120401.pdf
Gao JW, Yao K: Some concepts and theorems of uncertain random process. Int. J. Intell. Syst (2014 in press)
Hou YC: Subadditivity of chance measure. . http://orsc.edu.cn/online/130602.pdf