Determine the Optimal Bayesian Fuzzy Membership Function Using Fuzzy Data

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.