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Some inequalities and limit theorems for fuzzy random variables adopted with \(\alpha \)-values of fuzzy numbers

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Abstract

In this paper, some essential stochastic inequalities and several convergence theorems were investigated for fuzzy random variables. The classical counterpart relationship between the proposed convergence theorems was also discussed in the fuzzy environment. The main advantage of the proposed method is its minimal requirements for such limit theorems and inequalities compared to the conventional methods used in the fuzzy environments. The previous methods mostly rely on the lower and upper bounds of the \(\alpha \)-cuts of fuzzy random variables, while the proposed method utilizes a unified quantity called \(\alpha \)-value.

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Acknowledgements

The authors would like to thank the anonymous reviewer for his/her constructive suggestions and comments, which improved the presentation of this work.

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Authors and Affiliations

  1. Department of Statistics, Payame Noor University, Tehran, 19395-3697, Iran

    Gholamreza Hesamian

  2. Department of Statistics, University of Birjand, Birjand, 615-97175, Iran

    Mohammad Ghasem Akbari

  3. Department of Statistics, Golsetan University, Gorgan, 49138-15739, Iran

    Vahid Ranjbar

Authors
  1. Gholamreza Hesamian
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  2. Mohammad Ghasem Akbari
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  3. Vahid Ranjbar
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Correspondence to Mohammad Ghasem Akbari.

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Hesamian, G., Akbari, M.G. & Ranjbar, V. Some inequalities and limit theorems for fuzzy random variables adopted with \(\alpha \)-values of fuzzy numbers. Soft Comput 24, 3797–3807 (2020). https://doi.org/10.1007/s00500-019-04149-2

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