Cramér-Rao Lower Bound for Fuzzy-Valued Random Variables

Abstract

In some point estimation problems, we may confront imprecise (fuzzy) concepts. One important case is a situation where all observations are fuzzy rather than crisp. In this paper, using fuzzy set theory, we define a fuzzy-valued random variable, a fuzzy unbiased estimator, a fuzzy exponential family, and then we state and prove a Cramér-Rao lower bound for such fuzzy estimators. Finally, we give some examples.