Fuzzy Confidence Interval Estimation by Likelihood Ratio

We propose a fuzzy confidence interval estimation based on the likelihood ratio. This ratio, often used in hypotheses testing seems to be an efficient tool for calculating confidence intervals since it is known to be general, and thus can be applied on any parameter. The strength of the defended procedure is to use a wide range of estimators with any type of distribution for the estimation of confidence intervals when fuzziness occurs. The theoretical approach and the detailed steps of the calculation are given. This approach is illustrated by a classical problem: a fuzzy confidence interval for the fuzzy mean in the context of a normal distribution. Finally, a comparison between the interval by the defended approach and one calculated by a frequently used expression is made. Our results show that the support set of the fuzzy interval by the defended method is smaller than the one by the known expression.