This paper deals with optimal properties of fuzzy least squares estimators of the fuzzy linear regression model with fuzzy input-output data that has an error structure. Fuzzy least squares estimators with new operations for regression parameters were proposed earlier in our previous study based on a suitable metric, and shows that the estimators are fuzzy-type linear estimators. We propose expectations and variances by using the algebraic properties of the triangular fuzzy matrices, and show some optimal properties BLUE(Best Linear Unbiased Estimator) of the estimators. Simple computational example is given to confirm these properties.