Soft Computing

, Volume 22, Issue 17, pp 5817–5824 | Cite as

Complex uncertain random variables

  • Rong GaoEmail author
  • Zhiqiang Zhang
  • Hamed Ahmadazde
  • Dan A. Ralescu


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 


Compliance of ethical standards

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Rong Gao
    • 1
    Email author
  • Zhiqiang Zhang
    • 2
  • Hamed Ahmadazde
    • 3
  • Dan A. Ralescu
    • 4
  1. 1.School of Economics and ManagementHebei University of TechnologyTianjinChina
  2. 2.School of Mathematics and Computer ScienceShanxi Datong UniversityDatongChina
  3. 3.Department of StatisticsUniversity of Sistan and BaluchestanZahedanIran
  4. 4.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA

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