Non-asymptotic fuzzy estimators based on confidence intervals

In this paper, we study and generalize the method of fuzzy estimation which is based on confidence intervals. We provide definitions and the corresponding formulas. The method we propose allows new additional ways in constructing fuzzy estimators. In particular, instead of constructing fuzzy estimators as the exact set of confidence intervals of the parameters to be estimated, we generalize them, in such a way that we eliminate discontinuities, and ensure compact support preserving the statistically derived triangular shape of the estimators. Our approach is particularly useful in critical situations, where subtle fuzzy comparisons between almost equal statistical quantities have to be made. An example of this application is provided.