Abstarct: Statistical analysis, in traditional form, is baxsed on crispness of data, random variables, parameters, point estimations and testing statistical hypotheses. In some cases, these concepts are vaguely observed or reported, therefore theory of fuzzy sets is a well known tool for formulation and analysis of this concepts. In this study, we first present the basic concepts of fuzzy sets such as fuzzy random variables, fuzzy probability density function and mathematical expectation of fuzzy random variable. Then we described L2-metric and Yao-Wu signed distance and will discussed fuzzy uniformly minimum variance unbiased (UMVU) and Bayesian estimators by this two meters. Also we compare crisp Neyman-Pearson Lemma and generalized Neyman-Pearson Lemma in three fuzzy cases. In the end, we option a new maximum likelihood estimation on baxsed presented probability density function of the one cases.