Covariance is a measure to characterize the joint variability of two complex uncertain variables. Since, calculating covariance is not easy based on uncertain measure, we present two formulas for covariance and pseudo covariance of complex uncertain variables. For calculating the covariance of complex uncertain variables, some theorems are proved and several formulas are provided by using the inverse uncertainty distribution. The main results are explained by using several examples.
AhmadzadeH., ShengY.H. and HassantabarF., Some results of moments of uncertain random variables, Iranian Journal of Fuzzy Systems14(2) (2017), 1–21.
2.
AhmadzadeH., ShengY. and EsfahaniM., On the convergence of uncertain random sequences, Fuzzy Optimization and Decision Making16(2) (2017), 205–220.
3.
AhmadzadeH., GaoR. and NaderiH., On the convergence of complex uncertain random sequences, Journal of Intelligent and Fuzzy Systems35(2) (2018), 2459–2467.
4.
ChenX.M., NingY.F. and WangX., Convergence of complex uncertain sequences, Journal of Intelligent and Fuzzy Systems6 (2016), 3357–3366.
5.
ChenX.M., NingY.F. and WangX., Formulas to calculate the variance and Pseudo-variance of complex uncertain variable, Proceedings of the fourth international forum on decision sciences (2017), 361–376.
6.
GaoR., ZhangZ., AhmadazdeH. and RalescuD.A., Complex Uncertain Random Variables, Soft Computing22(17) (2018), 5817–5824.
7.
GaoR. and YaoK., Importance Index of Components in Uncertain Random Systems, Knowledge-Based Systems109 (2016), 208–217.
8.
GaoR. and RalescuD.A., Convergence in distribution for uncertain random variables, IEEE Transactions on Fuzzy Systems26(3) (2018), 1427–1434.
9.
GoodmanN.R., Statistial analysis based on a certain multivariate complex Gaussian distribution, Annals of Mathematics and Statistics34(1) (1963), 152–177.
10.
LiuB., Uncertainty Theory, 2nd ed, Springer-Verlag, Berlin (2007).
11.
LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems3(1) (2009), 3–10.
12.
LiuY.H. and HaM.H., Expected value of function of uncertain variables, Journal of Uncertain Systems4(3) (2010).
13.
LiuY.H., Uncertain random variables: A mixture of uncertainty and randomness, Soft Computing17(4) (2013), 625–634.
14.
PengZ.X., Complex uncertain variables, Doctoral Dissertation, Tsinghua University (2012).
15.
TurinG.L., The characteristic function of hermitian quadratic forms in complex normal variable, Biometrika47(1960), 199–201.
16.
WoodingR.A., The multivariate distribution of complex normal variable, Biometrica43(1956), 212–215.
17.
YaoK., A formula to calculate the variance of uncertain variable, Soft Computing19(10) (2015), 2947–2953.
18.
ZhaoM., LiuY., RalescuD.A. and ZhouJ., The Covariance of Uncertain Variables: Definition and Calculation Formulae, Fuzzy Optimization and Decision Making27(2) (2017), 211–232.
