In this paper, Bayesian fuzzy estimator is obtained first, for the fuzzy data based on the probability prior distribution and afterward based on the possible model and the possibility of a prior distribution. Considering the effect of the membership functions on the fuzzy and possibility Bayesian estimators, a membership function that gives the optimal fuzzy and possibility Bayesian estimators will be introduced for the data. The optimality of the new triangular-gaussian membership function is denoted by using the normal and exponential data sets.