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Totally ordered uncertain sets

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Abstract

It is known that some uncertain sets have membership functions, and some do not. How do we judge whether an uncertain set has a membership function? In order to answer this question, this paper presents a concept of totally ordered uncertain set, and shows that totally ordered uncertain sets always have membership functions if they are defined on a continuous uncertainty space. In addition, some criteria for judging the existence of membership functions for uncertain sets are provided. Several inspiring examples and counterexamples are also documented in this paper.

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References

  • 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 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)

  • 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.

    Book  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Liu, B. (2012a). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6(1), 3–10.

    Google Scholar 

  • Liu, B. (2012b). 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 

  • Peng, ZX., & Chen, XW. (2014) Uncertain systems are universal approximators, Journal of Uncertainty Analysis and Applications, 2(13)

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

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China Grant No.61573210.

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Authors and Affiliations

  1. Uncertainty Theory Laboratory, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Baoding Liu

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  1. Baoding Liu
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Correspondence to Baoding Liu.

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Liu, B. Totally ordered uncertain sets. Fuzzy Optim Decis Making 17, 1–11 (2018). https://doi.org/10.1007/s10700-016-9264-6

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  • DOI: https://doi.org/10.1007/s10700-016-9264-6

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