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A stronger law of large numbers for uncertain random variables

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Abstract

Uncertainty and randomness are two basic types of indeterminacy, which often appears simultaneously in practice. For modelling a complex system with not only uncertainty but also randomness, uncertain random variable is presented to describe the associated parameters and further chance measure is founded. An easy-to-handle case is to consider measurable functions of uncertain variables and random variables. This paper presents a stronger law of large numbers for such a case where random variables are independent but not identically distributed in probability measure and uncertain variables are also independent but not identically distributed in uncertain measure.

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Acknowledgements

This work was supported by National Natural Science Foundation of China Grant Nos. 61462086, 61563050 and 71371019 and was also supported by the Fundamental Research Funds for the Central Universities (No. YWF-16-BJY-20).

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Authors and Affiliations

  1. College of Mathematical and System Sciences, Xinjiang University, Urumqi, 830046, China

    Yuhong Sheng

  2. School of Information Science and Engineering, Xinjiang University, Urumqi, 830046, China

    Gang Shi

  3. Department of Computer Sciences, Tsinghua University, Beijing, 100084, China

    Gang Shi

  4. School of Economics and Management, Beihang University, Beijing, 100191, China

    Zhongfeng Qin

Authors
  1. Yuhong Sheng
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  2. Gang Shi
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  3. Zhongfeng Qin
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Corresponding author

Correspondence to Zhongfeng Qin.

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Yuhong Sheng, Gang Shi and Zhongfeng Qin declare that they have no conflict of interest.

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

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Communicated by Y. Ni.

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Sheng, Y., Shi, G. & Qin, Z. A stronger law of large numbers for uncertain random variables. Soft Comput 22, 5655–5662 (2018). https://doi.org/10.1007/s00500-017-2586-7

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  • DOI: https://doi.org/10.1007/s00500-017-2586-7

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