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Soft Computing

, Volume 22, Issue 13, pp 4347–4351 | Cite as

The pseudo-convergence of measurable functions on set-valued fuzzy measure space

  • Jian Rong Wu
  • Xiao Ni Geng
Foundations
  • 57 Downloads

Abstract

For sequences of measurable functions on a set-valued fuzzy measure space, the concepts of pseudo almost everywhere convergence, pseudo almost uniformly convergence, and pseudo-convergence in measure are introduced. Then, Egoroff’s theorem, Lebesgue’s theorem, and Riesz’s theorem are generalized from real-valued fuzzy measure spaces onto set-valued fuzzy measure spaces.

Keywords

Fuzzy analysis Set-valued fuzzy measure Measurable function Convergence theorem 

Notes

Acknowledgements

Jianrong Wu has been supported by National Natural Science Foundation of China (No. 11371013). The authors acknowledge the reviewer’s comments and suggestions very much, which are valuable in improving the quality of our manuscript.

Compliance with ethical standards

Conflict of interest

Both authors declare that they have no conflict of interest.

Human and animals participants

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

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Physics ScienceSuzhou University of Science and TechnologySuzhouPeople’s Republic of China

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