We propose two practical procedures to construct fuzzy confidence intervals with fuzzy observations. These procedures use the fuzzy extensions of the quantile function and the concept of fuzzy empirical distribution. With bootstrapping techniques, we first compute fuzzy empirical distributions of the parameter of interest. We then build fuzzy confidence intervals by either finding the fuzzy quantiles of the distribution directly or using the fuzzy quantile function to find the relevant fuzzy quantiles. Our methods are illustrated through a numerical application. We construct fuzzy confidence intervals with the advocated methods and compare them to the fuzzy traditional way of creating such intervals and their construction using the likelihood ratio as in Berkachy and Donzé [2].

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Fuzzy Confidence Intervals by Bootstrapped Fuzzy Distributions

  • Julien Rosset,
  • Laurent Donzé

摘要

We propose two practical procedures to construct fuzzy confidence intervals with fuzzy observations. These procedures use the fuzzy extensions of the quantile function and the concept of fuzzy empirical distribution. With bootstrapping techniques, we first compute fuzzy empirical distributions of the parameter of interest. We then build fuzzy confidence intervals by either finding the fuzzy quantiles of the distribution directly or using the fuzzy quantile function to find the relevant fuzzy quantiles. Our methods are illustrated through a numerical application. We construct fuzzy confidence intervals with the advocated methods and compare them to the fuzzy traditional way of creating such intervals and their construction using the likelihood ratio as in Berkachy and Donzé [2].