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