Testing fuzzy hypotheses based on fuzzy test statistic

  • Authors:

  • S. Mahmoud Taheri;Mohsen Arefi

  • Affiliations:

  • Isfahan University of Technology, Department of Mathematical Sciences, 84156-83111, Isfahan, Iran and Statistical Research and Training Center (SRTC), Tehran, Iran;Isfahan University of Technology, Department of Mathematical Sciences, 84156-83111, Isfahan, Iran

  • Venue:
  • Soft Computing - A Fusion of Foundations, Methodologies and Applications
  • Year:
  • 2009

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Abstract

A new approach for testing fuzzy parametric hypotheses based on fuzzy test statistic is introduced. First, we define some models representing the extended versions of the simple, the one-sided and the two-sided crisp hypotheses to the fuzzy ones. Then, we provide a confidence interval for interested parameter, and using α-cuts of the fuzzy null hypothesis, we construct the related fuzzy test statistic. Finally, by introducing a credit level, we can decide to accept or reject the fuzzy hypothesis. The method is applied to test the fuzzy hypotheses for the mean of a normal distribution, the variance of a normal distribution, and the mean of a Poisson distribution.