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Conditional uncertain set and conditional membership function

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Abstract

The uncertain set, as a generation of uncertain variable, is a set-valued function on an uncertainty space. The conditional uncertain set, derived from an uncertain set restricted to a conditional uncertainty space given an uncertain event, plays a crucial role in uncertain inference systems. This paper studies conditional uncertain sets and their membership functions, and gives a sufficient condition for an uncertain set having a conditional membership function. In addition, when the uncertain set is conditioned on an independent event, this paper finds the analytic expression of the conditional membership function based on the original membership function.

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References

  • Dai, W., & Chen, X. W. (2012). Entropy of function of uncertain variables. Mathematical and Computer Modelling, 55(3–4), 754–760.

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, X., Gao, Y., & Ralescu, D. A. (2010). On Liu’s inference rule for uncertain systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18(1), 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, Y. (2012). Uncertain inference control for balancing an inverted pendulum. Fuzzy Optimization and Decision Making, 11(4), 481–492.

    Article  MathSciNet  MATH  Google Scholar 

  • Guo, H. Y., Wang, X. S., Wang, L. L., & Chen, D. (2016). Delphi method for estimating membership function of uncertain set. Journal of Uncertainty Analysis and Applications, 4, 3.

    Article  Google Scholar 

  • Liu, B. (2007). Uncertainty Theory (2nd ed.). Berlin: Springer.

    MATH  Google Scholar 

  • Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.

    Google Scholar 

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

  • Liu, B. (2010b). Uncertain set theory and uncertain inference rule with application to uncertain control. Journal of Uncertain Systems, 4(2), 83–98.

  • Liu, B. (2011). Uncertain logic for modeling human language. Journal of Uncertain Systems, 5(1), 3–20.

    Google Scholar 

  • Liu, B. (2012). Membership functions and operational law of uncertain sets. Fuzzy Optimization and Decision Making, 11(4), 387–410.

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, B. (2013). A new definition of independence of uncertain sets. Fuzzy Optimization and Decision Making, 12(4), 451–461.

    Article  MathSciNet  Google Scholar 

  • Liu, B. (2015). Uncertainty theory (4th ed.). Berlin: Springer.

    MATH  Google Scholar 

  • Liu, B. (2016). Totally ordered uncertain sets. Fuzzy Optimization and Decision Making,. doi:10.1007/s10700-016-9264-6.

    Google Scholar 

  • Liu, Y. H., & Ha, M. H. (2010). Expected value of function of uncertain variables. Journal of Uncertain Systems, 4(3), 181–186.

    Google Scholar 

  • Peng, Z. X., & Iwamura, K. (2010). A sufficient and necessary condition of uncertainty distribution. Journal of Interdisciplinary Mathematics, 13(3), 277–285.

    Article  MathSciNet  MATH  Google Scholar 

  • Peng, Z. X., & Chen, X. W. (2014). Uncertain systems are universal approximiators. Journal of Uncertainty Analysis and Applications, 2, 13.

    Article  Google Scholar 

  • Wang, X. S., & Ha, M. H. (2013). Quadratic entropy of uncertain sets. Fuzzy Optimization and Decision Making, 12(1), 99–109.

    Article  MathSciNet  Google Scholar 

  • Yang, X. F., & Gao, J. (2014). A review on uncertain set. Journal of Uncertain Systems, 8(4), 285–300.

    MathSciNet  Google Scholar 

  • Yang, X. F., & Gao, J. (2015). Some results of moments of uncertain set. Journal of Intelligent and Fuzzy Systems, 28(6), 2433–2442.

    Article  MathSciNet  MATH  Google Scholar 

  • Yao, K., & Ke, H. (2014). Entropy operator for membership function of uncertain set. Applied Mathematics and Computation, 242, 898–906.

    Article  MathSciNet  MATH  Google Scholar 

  • Yao, K. (2014). Sine entropy of uncertain set and its applications. Applied Soft Computing, 22, 432–442.

    Article  Google Scholar 

  • Yao, K. (2015a). A formula to calculate the variance of uncertain variable. Soft Computing, 19(10), 2947–2953.

  • Yao, K. (2015b). Inclusion relationship of uncertain sets. Journal of Uncertainty Analysis and Applications, 3, 13.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61403360), the Special Funds for Science and Education Fusion of University of Chinese Academy of Sciences, and the Open Project of Key Laboratory of Big Data Mining and Knowledge Management of Chinese Academy of Sciences.

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Authors and Affiliations

  1. School of Economics and Management, University of Chinese Academy of Sciences, Beijing, 100190, China

    Kai Yao

  2. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, 100190, China

    Kai Yao

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  1. Kai Yao
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Correspondence to Kai Yao.

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Yao, K. Conditional uncertain set and conditional membership function. Fuzzy Optim Decis Making 17, 233–246 (2018). https://doi.org/10.1007/s10700-017-9271-2

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  • DOI: https://doi.org/10.1007/s10700-017-9271-2

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