One can identify at least two types of inexactness: one is randomness associated with frequencies and the other is uncertainty associated with belief degrees. However, randomness and uncertainty usually exist in a complex system simultaneously. To model such complex phenomena, we present a concept of complex uncertain random variable. Then, we derive the complex chance distributions of complex uncertain random variables. Moreover, the expected value and variance of a complex uncertain random variable are also studied. Finally, we define and study the complex linear and normal uncertain random variables.
Uncertainty theory Uncertain variable Uncertain random variable Chance distribution Complex variable
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The authors declare that there is no conflict of interests regarding the publication of this paper.
This article does not contain any studies with human participants performed by any of the authors.
Chen XM, Ning YF, Wang X (2016) Convergence of complex uncertain sequences. J Intell Fuzzy Syst 6:3357–3366CrossRefMATHGoogle Scholar
Chen XM, Ning YF, Wang X (2017) Formulas to calculate the variance and Pseudo-variance of complex uncertain variable. Proceedings of the fourth international forum on decision sciences pp 361–376Google Scholar
Gao R, Sheng YH (2016) Law of large numbers for uncertain random variables with different chance distributions. J Intell Fuzzy Syst 31(3):1227–1234MathSciNetCrossRefMATHGoogle Scholar
Gao R, Sun Y, Ralescu DA (2017) Order statistics of uncertain random variables with application to k-out-of-n System. Fuzzy Optim Decis Mak 16(2):159–181MathSciNetCrossRefGoogle Scholar
Gao R, Yao K (2016) Importance index of components in uncertain random systems. Knowl Based Syst 109:208–217CrossRefGoogle Scholar
Gao R, Yao K (2016) Importance index of components in uncertain reliability systems. J Uncertain Anal Appl 4:7CrossRefGoogle Scholar
Goodman NR (1963) Statistial analysis based on a certain multivariate complex Gaussian distribution. Ann Math Stat 34(1):152–177CrossRefMATHGoogle Scholar
Guo HY, Wang XS (2014) Variance of uncertain random variables. J Uncertain Anal Appl 2:6CrossRefGoogle Scholar