Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable


In this paper we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop an approach for normal fuzzy random variables, and two different approaches for the case of fuzzy random variables taking on a finite number of different values. A real-life example illustrates the use of the last two approaches. Finally, a comparison between the introduced techniques is developed by means of simulation studies leading to close inferential conclusions.

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Correspondence to María Ángeles Gil.

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Acknowledgements. The research in this paper has been partially supported by MCYT Grants BFM2002-01057 and BFM2001-3494. Their financial support is gratefully acknowledged. The authors are sincerely grateful to their colleague Gil González-Rodríguez for all his comments and suggestions in connection with this paper; his scientific support has been very valuable. The authors want also thank the referees of the first version of the paper because of their useful hints to improve it.

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Montenegro, M., Colubi, A., Rosa Casals, M. et al. Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika 59, 31–49 (2004).

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  • Boot strap
  • Distance between fuzzy numbers
  • Fuzzy random variables
  • Large Smaple Theory