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The covariance of uncertain variables: definition and calculation formulae

Author

Listed:
  • Mingxuan Zhao

    (Shanghai University)

  • Yuhan Liu

    (University of Cincinnati)

  • Dan A. Ralescu

    (University of Cincinnati)

  • Jian Zhou

    (Shanghai University)

Abstract

Uncertainty theory as a branch of axiomatic mathematics has been widely used to deal with human uncertainty. The two commonly used numerical characteristics of uncertain variables, the expected value and the variance together with their mathematical properties have been discussed and applied to real optimization problems in an uncertain environment. As a further study, in this paper, we focus on the covariance and correlation coefficient of uncertain variables. The definitions and calculation formulae of covariance and correlation coefficient of two uncertain variables are suggested by means of their inverse distributions. Then we show that the correlation coefficient of uncertain variables is essentially a measure of the relevance of distributions of uncertain variables. Finally, the relation between variance and covariance is analysed and represented with some equalities and inequalities.

Suggested Citation

  • Mingxuan Zhao & Yuhan Liu & Dan A. Ralescu & Jian Zhou, 2018. "The covariance of uncertain variables: definition and calculation formulae," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 211-232, June.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:2:d:10.1007_s10700-017-9270-3
    DOI: 10.1007/s10700-017-9270-3
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    References listed on IDEAS

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    1. Lin Chen & Jin Peng & Zhibing Liu & Ruiqing Zhao, 2017. "Pricing and effort decisions for a supply chain with uncertain information," International Journal of Production Research, Taylor & Francis Journals, vol. 55(1), pages 264-284, January.
    2. Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
    3. Jian Zhou & Yuanyuan Liu & Xiaoxia Zhang & Xin Gu & Di Wang, 2017. "Uncertain risk aversion," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 615-624, March.
    4. Shuya Zhong & Yizeng Chen & Jian Zhou & Yuanyuan Liu, 2017. "An interactive satisficing approach for multi-objective optimization with uncertain parameters," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 535-547, March.
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    Cited by:

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    2. Lu, Cheng & Teng, Da & Chen, Jun-Yu & Fei, Cheng-Wei & Keshtegar, Behrooz, 2023. "Adaptive vectorial surrogate modeling framework for multi-objective reliability estimation," Reliability Engineering and System Safety, Elsevier, vol. 234(C).

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