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A formula to calculate the variance of uncertain variable

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Uncertainty theory is a branch of axiomatic mathematics that deals with human uncertainty, and uncertain variable is used to model the uncertain quantities. Inverse uncertainty distribution provides an easy way to calculate the functions of uncertain variables as well as their expected values. This paper mainly presents a formula to calculate the variance of an uncertain variable via the inverse uncertainty distribution. Besides, some inequalities about the variance of uncertain variables are also derived.

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  • Chen XW, Dai W (2011) Maximum entropy principle for uncertain variables. Int J Fuzzy Syst 13(3):232–236

    MathSciNet  Google Scholar 

  • Chen XW, Kar S, Ralescu DA (2012) Cross-entropy measure of uncertain variables. Inf Sci 201:53–60

    Article  MATH  MathSciNet  Google Scholar 

  • Dai W, Chen XW (2012) Entropy of function of uncertain variables, mathematical and computer modelling 55(3–4):754–760

  • Dai W (2012) Quadratic entropy of uncertain variables. Inf Int Interdiscip J (to be published)

  • Gao X (2009) Some properties of continuous uncertain measure. Int J Uncertain Fuzziness Knowl Based Syst 17(3):419–426

    Article  MATH  Google Scholar 

  • Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47(2):263–292

    Article  MATH  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

  • Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

  • Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin

  • Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):3–10

    Google Scholar 

  • Liu W, Xu JP (2010) Some properties on expected value operator for uncertain variables. Inf Int Interdiscip J 13(5):1693–1699

  • Liu YH, Ha MH (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186

    Google Scholar 

  • Peng ZX, Iwamura K (2010) A sufficient and necessary condition of uncertainty distribution. J Interdiscip Math 13(3):277–285

    Article  MATH  MathSciNet  Google Scholar 

  • Yao K, Gao JW, Dai W (2013) Sine entropy for uncertain variable. Int J Uncertainty Fuzziness Knowl Based Syst 21(5):743–753

  • You CL (2009) Some convergence theorems of uncertain sequences. Math Comp Model 49(3–4):482–487

  • Zhang ZM (2011) Some discussions on uncertain measure. Fuzzy Optim Decis Making 10(1):31–43

    Article  MATH  Google Scholar 

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This work was supported by National Natural Science Foundation of China (Grant No. 61403360).

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Correspondence to Kai Yao.

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Communicated by V. Loia.

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Yao, K. A formula to calculate the variance of uncertain variable. Soft Comput 19, 2947–2953 (2015).

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